diff --git a/CHANGELOG.md b/CHANGELOG.md index 2ece800..b579788 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -9,6 +9,8 @@ the [Deprecations](https://hugofara.github.io/pylinkage/deprecations.html) page. ## [Unreleased] +## [1.3.0] - 2026-10-25 + ### Added - **Python 3.15 support.** It is tested in CI. On 3.15 the `cad` extra @@ -17,9 +19,12 @@ the [Deprecations](https://hugofara.github.io/pylinkage/deprecations.html) page. ### Changed -- **Breaking:** Dropped Python 3.10 support, which reached end of life in - October 2026. Minimum version is now Python 3.11. `typing_extensions` is no - longer a dependency. +- **Python 3.11 or later is required.** Python 3.10 reached end of life in + October 2026. pip keeps a 3.10 environment on 1.2.2. `typing_extensions` is + no longer a dependency. +- The development lockfile is refreshed. It moves pillow to 13.0.0, along with + certifi, tornado, urllib3 and nbconvert, past the advisories Dependabot + reported. None of them reach the published package. ### Fixed diff --git a/CITATION.cff b/CITATION.cff index 26bf532..535b173 100644 --- a/CITATION.cff +++ b/CITATION.cff @@ -7,8 +7,8 @@ authors: given-names: Hugo orcid: "https://orcid.org/0009-0001-0769-4434" affiliation: "Independent Researcher, France" -version: 1.2.2 -date-released: "2026-09-18" +version: 1.3.0 +date-released: "2026-10-25" identifiers: - type: doi value: "10.5281/zenodo.21207486" diff --git a/docs/_static/documentation_options.js b/docs/_static/documentation_options.js index 6b54cf4..2372992 100644 --- a/docs/_static/documentation_options.js +++ b/docs/_static/documentation_options.js @@ -1,5 +1,5 @@ const DOCUMENTATION_OPTIONS = { - VERSION: '1.2.2', + VERSION: '1.3.0', LANGUAGE: 'en', COLLAPSE_INDEX: false, BUILDER: 'html', diff --git a/docs/api/modules.html b/docs/api/modules.html index 2a08533..f402cab 100644 --- a/docs/api/modules.html +++ b/docs/api/modules.html @@ -6,14 +6,14 @@ - pylinkage — pylinkage 1.2.2 documentation + pylinkage — pylinkage 1.3.0 documentation - + diff --git a/docs/api/pylinkage.actuators.html b/docs/api/pylinkage.actuators.html index 60dd454..7ecd0d4 100644 --- a/docs/api/pylinkage.actuators.html +++ b/docs/api/pylinkage.actuators.html @@ -6,14 +6,14 @@ - pylinkage.actuators package — pylinkage 1.2.2 documentation + pylinkage.actuators package — pylinkage 1.3.0 documentation - + @@ -154,7 +154,7 @@

SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> arc_crank = ArcCrank(
 ...     anchor=O1,
 ...     radius=1.0,
@@ -263,6 +263,17 @@ 
Submodules
+

+set_coord(x: float | None, y: float | None) → None

+
Place the output, and read the crank angle from where it lands.

+
The angle is the direction from the anchor to (x, y), brought
+onto the arc; the sweep restarts in the positive direction, as it
+does on a new crank. Like a Crank, the arc crank is then
+entirely in the state its coordinates describe, so putting a
+linkage back in a position puts its actuators back too.

+

+
 
 
 
@@ -290,7 +301,7 @@ 
SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> crank.position
 (1.0, 0.0)
@@ -415,7 +426,7 @@ 
SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> actuator = LinearActuator(anchor=O1, angle=0.0, stroke=2.0, speed=0.1)
 >>> actuator.position
 (0.0, 0.0)
@@ -505,6 +516,18 @@ 
Submodules
+

+set_coord(x: float | None, y: float | None) → None

+
Place the output, and read the extension from where it lands.

+
The extension is the projection of (x, y) from the anchor
+onto the actuator’s axis, held within [0, stroke]; the stroke
+restarts in the extending direction, as it does on a new
+actuator. The actuator is then entirely in the state its
+coordinates describe, so putting a linkage back in a position
+puts its actuators back too.

+

+
 

 

 speed: float

@@ -535,7 +558,7 @@ 
Module contents
from pylinkage.components import Ground
 from pylinkage.actuators import Crank
 
-O1 = Ground(0.0, 0.0, name="O1")
+O1 = Ground(0.0, 0.0, name="O1")
 crank = Crank(anchor=O1, radius=1.0)
 

 

@@ -544,7 +567,7 @@ 
Module contentsfrom pylinkage.actuators import ArcCrank
 import math
 
-O1 = Ground(0.0, 0.0, name="O1")
+O1 = Ground(0.0, 0.0, name="O1")
 arc_crank = ArcCrank(anchor=O1, radius=1.0, arc_start=0, arc_end=math.pi/2)
 

 

@@ -552,7 +575,7 @@ 
Module contents
from pylinkage.components import Ground
 from pylinkage.actuators import LinearActuator
 
-O1 = Ground(0.0, 0.0, name="O1")
+O1 = Ground(0.0, 0.0, name="O1")
 actuator = LinearActuator(anchor=O1, angle=0.0, stroke=2.0, speed=0.1)
 

 

@@ -578,7 +601,7 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> arc_crank = ArcCrank(
 ...     anchor=O1,
 ...     radius=1.0,
@@ -687,6 +710,17 @@ 
Module contents
+

+set_coord(x: float | None, y: float | None) → None

+
Place the output, and read the crank angle from where it lands.

+
The angle is the direction from the anchor to (x, y), brought
+onto the arc; the sweep restarts in the positive direction, as it
+does on a new crank. Like a Crank, the arc crank is then
+entirely in the state its coordinates describe, so putting a
+linkage back in a position puts its actuators back too.

+

+
 
 
 

@@ -708,7 +742,7 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> crank.position
 (1.0, 0.0)
@@ -816,7 +850,7 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> actuator = LinearActuator(anchor=O1, angle=0.0, stroke=2.0, speed=0.1)
 >>> actuator.position
 (0.0, 0.0)
@@ -906,6 +940,18 @@ 
Module contents
+

+set_coord(x: float | None, y: float | None) → None

+
Place the output, and read the extension from where it lands.

+
The extension is the projection of (x, y) from the anchor
+onto the actuator’s axis, held within [0, stroke]; the stroke
+restarts in the extending direction, as it does on a new
+actuator. The actuator is then entirely in the state its
+coordinates describe, so putting a linkage back in a position
+puts its actuators back too.

+

+
 

 

 speed: float

diff --git a/docs/api/pylinkage.assur.html b/docs/api/pylinkage.assur.html
index f7eb9d1..d54ab5e 100644
--- a/docs/api/pylinkage.assur.html
+++ b/docs/api/pylinkage.assur.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.assur package — pylinkage 1.2.2 documentation
+  pylinkage.assur package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -307,8 +307,8 @@ 
Submodules>>> assur = AssurMechanism(mechanism)
 >>>
 >>> # Access formal properties
->>> print(f"DOF: {assur.degree_of_freedom}")
->>> print(f"Groups: {[g.joint_signature for g in assur.assur_groups]}")
+>>> print(f"DOF: {assur.degree_of_freedom}")
+>>> print(f"Groups: {[g.joint_signature for g in assur.assur_groups]}")
 >>>
 >>> # Simulation still works via delegation
 >>> for positions in assur.step():
@@ -553,10 +553,10 @@ 
SubmodulesExample

 
>>> result = decompose_assur_groups(graph)
->>> print(f"Ground: {result.ground}")
->>> print(f"Drivers: {result.drivers}")
+>>> print(f"Ground: {result.ground}")
+>>> print(f"Drivers: {result.drivers}")
 >>> for group in result.groups:
-...     print(f"  {group.joint_signature}: {group.internal_nodes}")
+...     print(f"  {group.joint_signature}: {group.internal_nodes}")
 

 

 

@@ -630,10 +630,10 @@ 
SubmodulesExample

-
>>> graph = LinkageGraph(name="Four-bar")
+
>>> graph = LinkageGraph(name="Four-bar")
 >>> # ... add nodes and edges ...
 >>> result = decompose_assur_groups(graph)
->>> print(f"Found {len(result.groups)} Assur groups")
+>>> print(f"Found {len(result.groups)} Assur groups")
 

 

 

@@ -681,7 +681,7 @@ 
SubmodulesExample

-
>>> edge = Edge("AB", source="A", target="B")
+
>>> edge = Edge("AB", source="A", target="B")
 

 

 

@@ -753,12 +753,12 @@ 
SubmodulesExample

-
>>> graph = LinkageGraph(name="Four-bar")
->>> graph.add_node(Node("A", role=NodeRole.GROUND))
->>> graph.add_node(Node("B", role=NodeRole.DRIVER))
->>> graph.add_edge(Edge("AB", source="A", target="B"))
->>> graph.neighbors("A")
-['B']
+
>>> graph = LinkageGraph(name="Four-bar")
+>>> graph.add_node(Node("A", role=NodeRole.GROUND))
+>>> graph.add_node(Node("B", role=NodeRole.DRIVER))
+>>> graph.add_edge(Edge("AB", source="A", target="B"))
+>>> graph.neighbors("A")
+['B']
 

 

 

@@ -947,7 +947,7 @@ 
SubmodulesExample

-
>>> node = Node("A", role=NodeRole.GROUND)
+
>>> node = Node("A", role=NodeRole.GROUND)
 >>> node.joint_type
 <JointType.REVOLUTE: 1>
 

@@ -1336,7 +1336,7 @@ 
SubmodulesExample

-
>>> hg = HypergraphLinkage(name="Four-bar")
+
>>> hg = HypergraphLinkage(name="Four-bar")
 >>> # ... add nodes and edges ...
 >>> assur_graph = from_hypergraph(hg)
 

@@ -1360,7 +1360,7 @@ 
SubmodulesExample

-
>>> assur_graph = LinkageGraph(name="Four-bar")
+
>>> assur_graph = LinkageGraph(name="Four-bar")
 >>> # ... add nodes and edges ...
 >>> hg = to_hypergraph(assur_graph)
 

@@ -1407,9 +1407,9 @@ 
SubmodulesExample

-
>>> graph = LinkageGraph(name="Four-bar")
->>> graph.add_node(Node("A", role=NodeRole.GROUND))
->>> dims = Dimensions(node_positions={"A": (0, 0)}, ...)
+
>>> graph = LinkageGraph(name="Four-bar")
+>>> graph.add_node(Node("A", role=NodeRole.GROUND))
+>>> dims = Dimensions(node_positions={"A": (0, 0)}, ...)
 >>> mechanism = graph_to_mechanism(graph, dims)
 >>> for positions in mechanism.step():
 ...     print(positions)
@@ -1507,8 +1507,8 @@ 
SubmodulesExample

-
>>> graph_to_json(graph, "my_linkage.json")
->>> restored = graph_from_json("my_linkage.json")
+
>>> graph_to_json(graph, "my_linkage.json")
+>>> restored = graph_from_json("my_linkage.json")
 

 

 

@@ -1547,8 +1547,8 @@ 
SubmodulesExample

-
>>> graph_to_json(graph, "my_linkage.json")
->>> restored = graph_from_json("my_linkage.json")
+
>>> graph_to_json(graph, "my_linkage.json")
+>>> restored = graph_from_json("my_linkage.json")
 

 

 

@@ -1595,14 +1595,14 @@ 
Submodules
>>> from pylinkage.assur import parse_signature, signature_to_hypergraph
 >>>
 >>> # Parse formal syntax
->>> sig = parse_signature("RRR")
+>>> sig = parse_signature("RRR")
 >>> print(sig.joint_signature)
-'RRR'
+'RRR'
 >>>
 >>> # Generate pure topology
 >>> graph = signature_to_hypergraph(sig)
 >>> print(list(graph.nodes.keys()))
-['anchor_0', 'anchor_1', 'internal_0']
+['anchor_0', 'anchor_1', 'internal_0']
 

 

 

@@ -1652,13 +1652,13 @@ 
SubmodulesExample

-
>>> sig = parse_signature("RRR")
+
>>> sig = parse_signature("RRR")
 >>> sig.joints
 (JointType.REVOLUTE, JointType.REVOLUTE, JointType.REVOLUTE)
 >>> sig.group_class
 <AssurGroupClass.DYAD: 1>
 >>> sig.canonical_form
-'RRR'
+'RRR'
 

 

 

@@ -1721,12 +1721,12 @@ 
SubmodulesExample

-
>>> isomer_to_canonical("RT_R")
-'RPR'
->>> isomer_to_canonical("T_R_T")
-'PRP'
->>> isomer_to_canonical("RRR")
-'RRR'
+
>>> isomer_to_canonical("RT_R")
+'RPR'
+>>> isomer_to_canonical("T_R_T")
+'PRP'
+>>> isomer_to_canonical("RRR")
+'RRR'
 

 

 

@@ -1753,16 +1753,16 @@ 
SubmodulesExample

-
>>> sig, roles = parse_isomer_signature("RT_R")
+
>>> sig, roles = parse_isomer_signature("RT_R")
 >>> sig
-'RT_R'
+'RT_R'
 >>> roles
-('revolute', 'slider', 'guide', 'revolute')
+('revolute', 'slider', 'guide', 'revolute')
 

 

-
>>> sig, roles = parse_isomer_signature("T_R_T")
+
>>> sig, roles = parse_isomer_signature("T_R_T")
 >>> roles
-('slider', 'guide', 'revolute', 'guide', 'slider')
+('slider', 'guide', 'revolute', 'guide', 'slider')
 

 

 

@@ -1788,19 +1788,19 @@ 
SubmodulesExample

-
>>> sig = parse_signature("RRR")
+
>>> sig = parse_signature("RRR")
 >>> sig.joints
 (JointType.REVOLUTE, JointType.REVOLUTE, JointType.REVOLUTE)
 

 

-
>>> sig = parse_signature("R_P_R")  # With separators
+
>>> sig = parse_signature("R_P_R")  # With separators
 >>> sig.canonical_form
-'RPR'
+'RPR'
 

 

-
>>> sig = parse_signature("RTR")  # T accepted as alias for P
+
>>> sig = parse_signature("RTR")  # T accepted as alias for P
 >>> sig.canonical_form
-'RPR'
+'RPR'
 

 

 

@@ -1820,15 +1820,15 @@ 
SubmodulesExample

-
>>> sig = parse_signature("RRR")
+
>>> sig = parse_signature("RRR")
 >>> cls = signature_to_group_class(sig)
 >>> cls.__name__
-'DyadRRR'
+'DyadRRR'
 

 

-
>>> cls = signature_to_group_class("RPR")
+
>>> cls = signature_to_group_class("RPR")
 >>> cls.__name__
-'DyadRPR'
+'DyadRPR'
 

 

 
@@ -1859,7 +1859,7 @@ 
SubmodulesExample

-
>>> graph = signature_to_hypergraph("RRR")
+
>>> graph = signature_to_hypergraph("RRR")
 >>> len(graph.nodes)
 3  # 2 anchors + 1 internal
 >>> len(graph.edges)
@@ -1867,8 +1867,8 @@ 
Submodules
>>> # With prefix for unique IDs
->>> leg = signature_to_hypergraph("RRR", prefix="leg1_")
->>> "leg1_anchor_0" in leg.nodes
+>>> leg = signature_to_hypergraph("RRR", prefix="leg1_")
+>>> "leg1_anchor_0" in leg.nodes
 True
 

 

@@ -1900,8 +1900,8 @@ 
Module contents>>> assur = AssurMechanism(mechanism)
 >>>
 >>> # Access structural properties
->>> print(f"DOF: {assur.degree_of_freedom}")
->>> print(f"Groups: {[g.joint_signature for g in assur.assur_groups]}")
+>>> print(f"DOF: {assur.degree_of_freedom}")
+>>> print(f"Groups: {[g.joint_signature for g in assur.assur_groups]}")
 >>>
 >>> # Simulation via delegation
 >>> for positions in assur.step():
@@ -2252,13 +2252,13 @@ 
Module contentsExample

-
>>> sig = parse_signature("RRR")
+
>>> sig = parse_signature("RRR")
 >>> sig.joints
 (JointType.REVOLUTE, JointType.REVOLUTE, JointType.REVOLUTE)
 >>> sig.group_class
 <AssurGroupClass.DYAD: 1>
 >>> sig.canonical_form
-'RRR'
+'RRR'
 

 

 

@@ -2325,10 +2325,10 @@ 
Module contentsExample

 
>>> result = decompose_assur_groups(graph)
->>> print(f"Ground: {result.ground}")
->>> print(f"Drivers: {result.drivers}")
+>>> print(f"Ground: {result.ground}")
+>>> print(f"Drivers: {result.drivers}")
 >>> for group in result.groups:
-...     print(f"  {group.joint_signature}: {group.internal_nodes}")
+...     print(f"  {group.joint_signature}: {group.internal_nodes}")
 

 

 

@@ -2512,7 +2512,7 @@ 
Module contentsExample

-
>>> edge = Edge("AB", source="A", target="B")
+
>>> edge = Edge("AB", source="A", target="B")
 

 

 

@@ -2629,12 +2629,12 @@ 
Module contentsExample

-
>>> graph = LinkageGraph(name="Four-bar")
->>> graph.add_node(Node("A", role=NodeRole.GROUND))
->>> graph.add_node(Node("B", role=NodeRole.DRIVER))
->>> graph.add_edge(Edge("AB", source="A", target="B"))
->>> graph.neighbors("A")
-['B']
+
>>> graph = LinkageGraph(name="Four-bar")
+>>> graph.add_node(Node("A", role=NodeRole.GROUND))
+>>> graph.add_node(Node("B", role=NodeRole.DRIVER))
+>>> graph.add_edge(Edge("AB", source="A", target="B"))
+>>> graph.neighbors("A")
+['B']
 

 

 

@@ -2823,7 +2823,7 @@ 
Module contentsExample

-
>>> node = Node("A", role=NodeRole.GROUND)
+
>>> node = Node("A", role=NodeRole.GROUND)
 >>> node.joint_type
 <JointType.REVOLUTE: 1>
 

@@ -2973,10 +2973,10 @@ 
Module contentsExample

-
>>> graph = LinkageGraph(name="Four-bar")
+
>>> graph = LinkageGraph(name="Four-bar")
 >>> # ... add nodes and edges ...
 >>> result = decompose_assur_groups(graph)
->>> print(f"Found {len(result.groups)} Assur groups")
+>>> print(f"Found {len(result.groups)} Assur groups")
 

 

 

@@ -3000,7 +3000,7 @@ 
Module contentsExample

-
>>> hg = HypergraphLinkage(name="Four-bar")
+
>>> hg = HypergraphLinkage(name="Four-bar")
 >>> # ... add nodes and edges ...
 >>> assur_graph = from_hypergraph(hg)
 

@@ -3039,8 +3039,8 @@ 
Module contentsExample

-
>>> graph_to_json(graph, "my_linkage.json")
->>> restored = graph_from_json("my_linkage.json")
+
>>> graph_to_json(graph, "my_linkage.json")
+>>> restored = graph_from_json("my_linkage.json")
 

 

 

@@ -3079,8 +3079,8 @@ 
Module contentsExample

-
>>> graph_to_json(graph, "my_linkage.json")
->>> restored = graph_from_json("my_linkage.json")
+
>>> graph_to_json(graph, "my_linkage.json")
+>>> restored = graph_from_json("my_linkage.json")
 

 

 

@@ -3114,9 +3114,9 @@ 
Module contentsExample

-
>>> graph = LinkageGraph(name="Four-bar")
->>> graph.add_node(Node("A", role=NodeRole.GROUND))
->>> dims = Dimensions(node_positions={"A": (0, 0)}, ...)
+
>>> graph = LinkageGraph(name="Four-bar")
+>>> graph.add_node(Node("A", role=NodeRole.GROUND))
+>>> dims = Dimensions(node_positions={"A": (0, 0)}, ...)
 >>> mechanism = graph_to_mechanism(graph, dims)
 >>> for positions in mechanism.step():
 ...     print(positions)
@@ -3167,19 +3167,19 @@ 
Module contentsExample

-
>>> sig = parse_signature("RRR")
+
>>> sig = parse_signature("RRR")
 >>> sig.joints
 (JointType.REVOLUTE, JointType.REVOLUTE, JointType.REVOLUTE)
 

 

-
>>> sig = parse_signature("R_P_R")  # With separators
+
>>> sig = parse_signature("R_P_R")  # With separators
 >>> sig.canonical_form
-'RPR'
+'RPR'
 

 

-
>>> sig = parse_signature("RTR")  # T accepted as alias for P
+
>>> sig = parse_signature("RTR")  # T accepted as alias for P
 >>> sig.canonical_form
-'RPR'
+'RPR'
 

 

 

@@ -3199,15 +3199,15 @@ 
Module contentsExample

-
>>> sig = parse_signature("RRR")
+
>>> sig = parse_signature("RRR")
 >>> cls = signature_to_group_class(sig)
 >>> cls.__name__
-'DyadRRR'
+'DyadRRR'
 

 

-
>>> cls = signature_to_group_class("RPR")
+
>>> cls = signature_to_group_class("RPR")
 >>> cls.__name__
-'DyadRPR'
+'DyadRPR'
 

 

 
@@ -3238,7 +3238,7 @@ 
Module contentsExample

-
>>> graph = signature_to_hypergraph("RRR")
+
>>> graph = signature_to_hypergraph("RRR")
 >>> len(graph.nodes)
 3  # 2 anchors + 1 internal
 >>> len(graph.edges)
@@ -3246,8 +3246,8 @@ 
Module contents
>>> # With prefix for unique IDs
->>> leg = signature_to_hypergraph("RRR", prefix="leg1_")
->>> "leg1_anchor_0" in leg.nodes
+>>> leg = signature_to_hypergraph("RRR", prefix="leg1_")
+>>> "leg1_anchor_0" in leg.nodes
 True
 

 

@@ -3270,7 +3270,7 @@ 
Module contentsExample

-
>>> assur_graph = LinkageGraph(name="Four-bar")
+
>>> assur_graph = LinkageGraph(name="Four-bar")
 >>> # ... add nodes and edges ...
 >>> hg = to_hypergraph(assur_graph)
 

diff --git a/docs/api/pylinkage.bridge.html b/docs/api/pylinkage.bridge.html
index 7e2c8cc..7c2e5c9 100644
--- a/docs/api/pylinkage.bridge.html
+++ b/docs/api/pylinkage.bridge.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.bridge package — pylinkage 1.2.2 documentation
+  pylinkage.bridge package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/api/pylinkage.cam.html b/docs/api/pylinkage.cam.html
index f286566..1b66f83 100644
--- a/docs/api/pylinkage.cam.html
+++ b/docs/api/pylinkage.cam.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.cam package — pylinkage 1.2.2 documentation
+  pylinkage.cam package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/api/pylinkage.components.html b/docs/api/pylinkage.components.html
index e69e9ed..89b0cac 100644
--- a/docs/api/pylinkage.components.html
+++ b/docs/api/pylinkage.components.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.components package — pylinkage 1.2.2 documentation
+  pylinkage.components package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -141,8 +141,8 @@ 
SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> O1.position
 (0.0, 0.0)
 

@@ -201,16 +201,16 @@ 
SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> crank = Crank(anchor=O1, radius=1.0)
->>> O2 = Ground(2.0, 0.0, name="O2")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> # Track a point at 45 degrees from crank->O2 line
 >>> tracker = PointTracker(
 ...     anchor1=crank.output,
 ...     anchor2=O2,
 ...     distance=0.5,
 ...     angle=math.pi/4,
-...     name="tracer_point"
+...     name="tracer_point"
 ... )
 

 

@@ -433,8 +433,8 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> O1.position
 (0.0, 0.0)
 

@@ -486,16 +486,16 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
 >>> crank = Crank(anchor=O1, radius=1.0)
->>> O2 = Ground(2.0, 0.0, name="O2")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> # Track a point at 45 degrees from crank->O2 line
 >>> tracker = PointTracker(
 ...     anchor1=crank.output,
 ...     anchor2=O2,
 ...     distance=0.5,
 ...     angle=math.pi/4,
-...     name="tracer_point"
+...     name="tracer_point"
 ... )
 

 

diff --git a/docs/api/pylinkage.dyads.html b/docs/api/pylinkage.dyads.html
index 015def9..5671cb4 100644
--- a/docs/api/pylinkage.dyads.html
+++ b/docs/api/pylinkage.dyads.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.dyads package — pylinkage 1.2.2 documentation
+  pylinkage.dyads package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -181,30 +181,30 @@ 
SubmodulesExamples

 
>>> # Circle-circle (RRR)
 >>> dyad = create_dyad(
-...     signature="RRR",
-...     anchors={"anchor1": crank.output, "anchor2": ground2},
-...     constraints={"distance1": 2.0, "distance2": 1.5},
-...     name="rocker",
+...     signature="RRR",
+...     anchors={"anchor1": crank.output, "anchor2": ground2},
+...     constraints={"distance1": 2.0, "distance2": 1.5},
+...     name="rocker",
 ... )
 

 

 
>>> # Circle-line (RT_R - slider crank)
 >>> dyad = create_dyad(
-...     signature="RT_R",
-...     anchors={"revolute": crank.output, "line1": L1, "line2": L2},
-...     constraints={"distance": 1.5},
-...     name="slider",
+...     signature="RT_R",
+...     anchors={"revolute": crank.output, "line1": L1, "line2": L2},
+...     constraints={"distance": 1.5},
+...     name="slider",
 ... )
 

 

 
>>> # Line-line (T_R_T - double slider)
 >>> dyad = create_dyad(
-...     signature="T_R_T",
+...     signature="T_R_T",
 ...     anchors={
-...         "line1_p1": A, "line1_p2": B,
-...         "line2_p1": C, "line2_p2": D,
+...         "line1_p1": A, "line1_p2": B,
+...         "line2_p1": C, "line2_p2": D,
 ...     },
-...     name="double_slider",
+...     name="double_slider",
 ... )
 

 

@@ -291,8 +291,8 @@ 
SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> # Create a point at 90 degrees from crank->O2 line
 >>> fixed = FixedDyad(
@@ -300,7 +300,7 @@ 
Submodules...     anchor2=O2,
 ...     distance=1.0,
 ...     angle=math.pi/2,
-...     name="coupler_point"
+...     name="coupler_point"
 ... )
 

 

@@ -390,8 +390,8 @@ 
Submodules>>> from pylinkage.cam import FunctionProfile, CycloidalMotionLaw
 >>> import math
 >>>
->>> O_cam = Ground(0.0, 0.0, name="cam_center")
->>> O_pivot = Ground(2.0, 0.0, name="pivot")
+>>> O_cam = Ground(0.0, 0.0, name="cam_center")
+>>> O_pivot = Ground(2.0, 0.0, name="pivot")
 >>> cam = Crank(anchor=O_cam, radius=0.1, angular_velocity=0.1)
 >>> # Profile: maps cam angle to arm angle offset (radians)
 >>> profile = FunctionProfile(
@@ -541,16 +541,16 @@ 
SubmodulesExample

-
>>> A = Ground(0.0, 0.0, name="A")
->>> B = Ground(2.0, 0.0, name="B")
->>> C = Ground(0.0, 1.0, name="C")
->>> D = Ground(2.0, 2.0, name="D")
+
>>> A = Ground(0.0, 0.0, name="A")
+>>> B = Ground(2.0, 0.0, name="B")
+>>> C = Ground(0.0, 1.0, name="C")
+>>> D = Ground(2.0, 2.0, name="D")
 >>> joint = PPDyad(
 ...     line1_anchor1=A,
 ...     line1_anchor2=B,
 ...     line2_anchor1=C,
 ...     line2_anchor2=D,
-...     name="intersection"
+...     name="intersection"
 ... )
 

 

@@ -650,16 +650,16 @@ 
SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> L1 = Ground(0.0, 1.0, name="L1")
->>> L2 = Ground(2.0, 1.0, name="L2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> L1 = Ground(0.0, 1.0, name="L1")
+>>> L2 = Ground(2.0, 1.0, name="L2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> slider = RRPDyad(
 ...     revolute_anchor=crank.output,
 ...     line_anchor1=L1,
 ...     line_anchor2=L2,
 ...     distance=1.5,
-...     name="slider"
+...     name="slider"
 ... )
 

 

@@ -756,15 +756,15 @@ 
SubmodulesExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> rocker = RRRDyad(
 ...     anchor1=crank.output,
 ...     anchor2=O2,
 ...     distance1=2.0,
 ...     distance2=1.5,
-...     name="rocker"
+...     name="rocker"
 ... )
 

 

@@ -859,14 +859,14 @@ 
Submodules>>> from pylinkage.cam import FunctionProfile, HarmonicMotionLaw
 >>> import math
 >>>
->>> O = Ground(0.0, 0.0, name="cam_center")
+>>> O = Ground(0.0, 0.0, name="cam_center")
 >>> cam = Crank(anchor=O, radius=0.1, angular_velocity=0.1)
 >>> profile = FunctionProfile(
 ...     motion_law=HarmonicMotionLaw(),
 ...     base_radius=1.0,
 ...     total_lift=0.5,
 ... )
->>> guide = Ground(0.0, 0.0, name="guide")
+>>> guide = Ground(0.0, 0.0, name="guide")
 >>> follower = TranslatingCamFollower(
 ...     cam_driver=cam,
 ...     profile=profile,
@@ -999,8 +999,8 @@ 
Module contentsfrom pylinkage.simulation import Linkage
 
 # Ground points
-O1 = Ground(0.0, 0.0, name="O1")
-O2 = Ground(2.0, 0.0, name="O2")
+O1 = Ground(0.0, 0.0, name="O1")
+O2 = Ground(2.0, 0.0, name="O2")
 
 # Crank (driver)
 crank = Crank(anchor=O1, radius=1.0, angular_velocity=0.1)
@@ -1014,7 +1014,7 @@ 
Module contents)
 
 # Build and simulate
-linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
+linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
 for positions in linkage.step():
     print(positions)
 

@@ -1074,8 +1074,8 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> # Create a point at 90 degrees from crank->O2 line
 >>> fixed = FixedDyad(
@@ -1083,7 +1083,7 @@ 
Module contents...     anchor2=O2,
 ...     distance=1.0,
 ...     angle=math.pi/2,
-...     name="coupler_point"
+...     name="coupler_point"
 ... )
 

 

@@ -1166,8 +1166,8 @@ 
Module contents>>> from pylinkage.cam import FunctionProfile, CycloidalMotionLaw
 >>> import math
 >>>
->>> O_cam = Ground(0.0, 0.0, name="cam_center")
->>> O_pivot = Ground(2.0, 0.0, name="pivot")
+>>> O_cam = Ground(0.0, 0.0, name="cam_center")
+>>> O_pivot = Ground(2.0, 0.0, name="pivot")
 >>> cam = Crank(anchor=O_cam, radius=0.1, angular_velocity=0.1)
 >>> # Profile: maps cam angle to arm angle offset (radians)
 >>> profile = FunctionProfile(
@@ -1310,16 +1310,16 @@ 
Module contentsExample

-
>>> A = Ground(0.0, 0.0, name="A")
->>> B = Ground(2.0, 0.0, name="B")
->>> C = Ground(0.0, 1.0, name="C")
->>> D = Ground(2.0, 2.0, name="D")
+
>>> A = Ground(0.0, 0.0, name="A")
+>>> B = Ground(2.0, 0.0, name="B")
+>>> C = Ground(0.0, 1.0, name="C")
+>>> D = Ground(2.0, 2.0, name="D")
 >>> joint = PPDyad(
 ...     line1_anchor1=A,
 ...     line1_anchor2=B,
 ...     line2_anchor1=C,
 ...     line2_anchor2=D,
-...     name="intersection"
+...     name="intersection"
 ... )
 

 

@@ -1413,16 +1413,16 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> L1 = Ground(0.0, 1.0, name="L1")
->>> L2 = Ground(2.0, 1.0, name="L2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> L1 = Ground(0.0, 1.0, name="L1")
+>>> L2 = Ground(2.0, 1.0, name="L2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> slider = RRPDyad(
 ...     revolute_anchor=crank.output,
 ...     line_anchor1=L1,
 ...     line_anchor2=L2,
 ...     distance=1.5,
-...     name="slider"
+...     name="slider"
 ... )
 

 

@@ -1513,15 +1513,15 @@ 
Module contentsExample

-
>>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> rocker = RRRDyad(
 ...     anchor1=crank.output,
 ...     anchor2=O2,
 ...     distance1=2.0,
 ...     distance2=1.5,
-...     name="rocker"
+...     name="rocker"
 ... )
 

 

@@ -1609,14 +1609,14 @@ 
Module contents>>> from pylinkage.cam import FunctionProfile, HarmonicMotionLaw
 >>> import math
 >>>
->>> O = Ground(0.0, 0.0, name="cam_center")
+>>> O = Ground(0.0, 0.0, name="cam_center")
 >>> cam = Crank(anchor=O, radius=0.1, angular_velocity=0.1)
 >>> profile = FunctionProfile(
 ...     motion_law=HarmonicMotionLaw(),
 ...     base_radius=1.0,
 ...     total_lift=0.5,
 ... )
->>> guide = Ground(0.0, 0.0, name="guide")
+>>> guide = Ground(0.0, 0.0, name="guide")
 >>> follower = TranslatingCamFollower(
 ...     cam_driver=cam,
 ...     profile=profile,
@@ -1753,30 +1753,30 @@ 
Module contentsExamples

 
>>> # Circle-circle (RRR)
 >>> dyad = create_dyad(
-...     signature="RRR",
-...     anchors={"anchor1": crank.output, "anchor2": ground2},
-...     constraints={"distance1": 2.0, "distance2": 1.5},
-...     name="rocker",
+...     signature="RRR",
+...     anchors={"anchor1": crank.output, "anchor2": ground2},
+...     constraints={"distance1": 2.0, "distance2": 1.5},
+...     name="rocker",
 ... )
 

 

 
>>> # Circle-line (RT_R - slider crank)
 >>> dyad = create_dyad(
-...     signature="RT_R",
-...     anchors={"revolute": crank.output, "line1": L1, "line2": L2},
-...     constraints={"distance": 1.5},
-...     name="slider",
+...     signature="RT_R",
+...     anchors={"revolute": crank.output, "line1": L1, "line2": L2},
+...     constraints={"distance": 1.5},
+...     name="slider",
 ... )
 

 

 
>>> # Line-line (T_R_T - double slider)
 >>> dyad = create_dyad(
-...     signature="T_R_T",
+...     signature="T_R_T",
 ...     anchors={
-...         "line1_p1": A, "line1_p2": B,
-...         "line2_p1": C, "line2_p2": D,
+...         "line1_p1": A, "line1_p2": B,
+...         "line2_p1": C, "line2_p2": D,
 ...     },
-...     name="double_slider",
+...     name="double_slider",
 ... )
 

 

diff --git a/docs/api/pylinkage.geometry.html b/docs/api/pylinkage.geometry.html
index b21b79f..10fc655 100644
--- a/docs/api/pylinkage.geometry.html
+++ b/docs/api/pylinkage.geometry.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.geometry package — pylinkage 1.2.2 documentation
+  pylinkage.geometry package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/api/pylinkage.html b/docs/api/pylinkage.html
index 240339c..1654579 100644
--- a/docs/api/pylinkage.html
+++ b/docs/api/pylinkage.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage package — pylinkage 1.2.2 documentation
+  pylinkage package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -153,6 +153,7 @@ 
SubpackagesArcCrank.radius
 
  • ArcCrank.reload()
    • 
 
  • ArcCrank.set_constraints()
    • 
+
  • ArcCrank.set_coord()
    • 
 
 
 
@@ -184,6 +185,7 @@ 
    SubpackagesLinearActuator.output
 
  • LinearActuator.reload()
    • 
 
  • LinearActuator.set_constraints()
    • 
+
  • LinearActuator.set_coord()
    • 
 
  • LinearActuator.speed
    • 
 
  • LinearActuator.stroke
    • 
 
@@ -967,6 +969,7 @@ 
    SubpackagesArcDriverLink.motor_joint
 
  • ArcDriverLink.output_joint
    • 
 
  • ArcDriverLink.radius
    • 
+
  • ArcDriverLink.read_angle()
    • 
 
  • ArcDriverLink.reset()
    • 
 
  • ArcDriverLink.step()
    • 
 
@@ -979,6 +982,7 @@ 
    SubpackagesDriverLink.motor_joint
 
  • DriverLink.output_joint
    • 
 
  • DriverLink.radius
    • 
+
  • DriverLink.read_angle()
    • 
 
  • DriverLink.reset()
    • 
 
  • DriverLink.step()
    • 
 
@@ -1796,9 +1800,9 @@ 
    SubmodulesExample
    
 
    >>> dims = Dimensions(
-...     node_positions={"A": (0.0, 0.0), "B": (1.0, 0.0)},
-...     driver_angles={"B": DriverAngle(0.1, 0.0)},
-...     edge_distances={"AB": 1.0},
+...     node_positions={"A": (0.0, 0.0), "B": (1.0, 0.0)},
+...     driver_angles={"B": DriverAngle(0.1, 0.0)},
+...     edge_distances={"AB": 1.0},
 ... )
 
    
 
    
@@ -1938,9 +1942,9 @@ 
    SubmodulesExample
    
-
    >>> dims = Dimensions(node_positions={"A": (0, 0), "X": (1, 1)})
->>> errors = dims.validate_against(["A", "B"], ["AB"])
->>> "X" in errors[0]  # "X" is not a valid node
+
    >>> dims = Dimensions(node_positions={"A": (0, 0), "X": (1, 1)})
+>>> errors = dims.validate_against(["A", "B"], ["AB"])
+>>> "X" in errors[0]  # "X" is not a valid node
 True
 
    
 
    
@@ -2050,7 +2054,7 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
 >>> arc_crank = ArcCrank(
 ...     anchor=O1,
 ...     radius=1.0,
@@ -2159,6 +2163,17 @@ 
    Module contents
+
    
+set_coord(x: float | None, y: float | None) → None
    
+
    Place the output, and read the crank angle from where it lands.
    
+
    The angle is the direction from the anchor to (x, y), brought
+onto the arc; the sweep restarts in the positive direction, as it
+does on a new crank. Like a Crank, the arc crank is then
+entirely in the state its coordinates describe, so putting a
+linkage back in a position puts its actuators back too.
    
+
    
+
 
 
 
    
@@ -2186,7 +2201,7 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> crank.position
 (1.0, 0.0)
@@ -2300,8 +2315,8 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> # Create a point at 90 degrees from crank->O2 line
 >>> fixed = FixedDyad(
@@ -2309,7 +2324,7 @@ 
    Module contents...     anchor2=O2,
 ...     distance=1.0,
 ...     angle=math.pi/2,
-...     name="coupler_point"
+...     name="coupler_point"
 ... )
 
    
 
    
@@ -2372,8 +2387,8 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> O1.position
 (0.0, 0.0)
 
    
@@ -2463,7 +2478,7 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
 >>> actuator = LinearActuator(anchor=O1, angle=0.0, stroke=2.0, speed=0.1)
 >>> actuator.position
 (0.0, 0.0)
@@ -2553,6 +2568,18 @@ 
    Module contents
+
    
+set_coord(x: float | None, y: float | None) → None
    
+
    Place the output, and read the extension from where it lands.
    
+
    The extension is the projection of (x, y) from the anchor
+onto the actuator’s axis, held within [0, stroke]; the stroke
+restarts in the extending direction, as it does on a new
+actuator. The actuator is then entirely in the state its
+coordinates describe, so putting a linkage back in a position
+puts its actuators back too.
    
+
    
+
 
    
 
    
 speed: float
    
@@ -2579,11 +2606,11 @@ 
    Module contents>>> from pylinkage.dyads import RRRDyad
 >>> from pylinkage.simulation import Linkage
 >>>
->>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0, angular_velocity=0.1)
 >>> rocker = RRRDyad(crank.output, O2, distance1=2.0, distance2=1.5)
->>> linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
+>>> linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
 >>> for positions in linkage.step():
 ...     print(positions)
 
    
@@ -2791,7 +2818,7 @@ 
    Module contentsExample
    
 
    >>> linkage.set_input_velocity(crank, omega=10.0)  # 10 rad/s
 >>> for pos, vel, acc in linkage.step_with_derivatives():
-...     print(f"Position: {pos}, Velocity: {vel}")
+...     print(f"Position: {pos}, Velocity: {vel}")
 
    
 
    
 
@@ -2890,7 +2917,7 @@ 
    Module contentsExample
    
 
    >>> linkage.set_input_velocity(crank, omega=10.0)
 >>> for pos, vel, acc in linkage.step_with_derivatives():
-...     print(f"Crank velocity: {vel[2]}")
+...     print(f"Crank velocity: {vel[2]}")
 
    
 
    
 
@@ -2992,16 +3019,16 @@ 
    Module contentsExample
    
-
    >>> A = Ground(0.0, 0.0, name="A")
->>> B = Ground(2.0, 0.0, name="B")
->>> C = Ground(0.0, 1.0, name="C")
->>> D = Ground(2.0, 2.0, name="D")
+
    >>> A = Ground(0.0, 0.0, name="A")
+>>> B = Ground(2.0, 0.0, name="B")
+>>> C = Ground(0.0, 1.0, name="C")
+>>> D = Ground(2.0, 2.0, name="D")
 >>> joint = PPDyad(
 ...     line1_anchor1=A,
 ...     line1_anchor2=B,
 ...     line2_anchor1=C,
 ...     line2_anchor2=D,
-...     name="intersection"
+...     name="intersection"
 ... )
 
    
 
    
@@ -3099,16 +3126,16 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
 >>> crank = Crank(anchor=O1, radius=1.0)
->>> O2 = Ground(2.0, 0.0, name="O2")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> # Track a point at 45 degrees from crank->O2 line
 >>> tracker = PointTracker(
 ...     anchor1=crank.output,
 ...     anchor2=O2,
 ...     distance=0.5,
 ...     angle=math.pi/4,
-...     name="tracer_point"
+...     name="tracer_point"
 ... )
 
    
 
    
@@ -3205,16 +3232,16 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
->>> L1 = Ground(0.0, 1.0, name="L1")
->>> L2 = Ground(2.0, 1.0, name="L2")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
+>>> L1 = Ground(0.0, 1.0, name="L1")
+>>> L2 = Ground(2.0, 1.0, name="L2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> slider = RRPDyad(
 ...     revolute_anchor=crank.output,
 ...     line_anchor1=L1,
 ...     line_anchor2=L2,
 ...     distance=1.5,
-...     name="slider"
+...     name="slider"
 ... )
 
    
 
    
@@ -3305,15 +3332,15 @@ 
    Module contentsExample
    
-
    >>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+
    >>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0)
 >>> rocker = RRRDyad(
 ...     anchor1=crank.output,
 ...     anchor2=O2,
 ...     distance1=2.0,
 ...     distance2=1.5,
-...     name="rocker"
+...     name="rocker"
 ... )
 
    
 
    
@@ -3553,7 +3580,10 @@ 
    Module contentspylinkage.kinematic_default_test(func: Callable[[...], float], error_penalty: float) → Callable[[Linkage, Iterable[float], JointPositions | None], float]
 
    Standard run for any linkage before a complete fitness evaluation.
    
 
    This decorator makes a kinematic simulation, before passing the loci to the
-decorated function.
    
+decorated function: one complete cycle of the linkage from its initial
+position, at the stride step() uses (dt=1), with at least 96
+frames. An evaluation therefore costs linkage.get_rotation_period()
+steps, the least common multiple of the actuators’ periods.
    
 
    
 
    Parameters:
    
 
    
 
    Anything else raises NotImplementedError so callers know to
 extend the bridge when pylinkage grows new component types.
    
@@ -1292,20 +1312,20 @@ 
    Module contentsfrom pylinkage.dimensions import Dimensions, DriverAngle
 
 # Create topology
-hg = HypergraphLinkage(name="Four-bar")
-hg.add_node(Node("A", role=NodeRole.GROUND))
-hg.add_node(Node("B", role=NodeRole.DRIVER))
-hg.add_node(Node("C", role=NodeRole.DRIVEN))
-hg.add_node(Node("D", role=NodeRole.GROUND))
-hg.add_edge(Edge("AB", "A", "B"))
-hg.add_edge(Edge("BC", "B", "C"))
-hg.add_edge(Edge("CD", "C", "D"))
+hg = HypergraphLinkage(name="Four-bar")
+hg.add_node(Node("A", role=NodeRole.GROUND))
+hg.add_node(Node("B", role=NodeRole.DRIVER))
+hg.add_node(Node("C", role=NodeRole.DRIVEN))
+hg.add_node(Node("D", role=NodeRole.GROUND))
+hg.add_edge(Edge("AB", "A", "B"))
+hg.add_edge(Edge("BC", "B", "C"))
+hg.add_edge(Edge("CD", "C", "D"))
 
 # Create dimensions
 dims = Dimensions(
-    node_positions={"A": (0, 0), "B": (1, 0), "C": (2, 1), "D": (3, 0)},
-    driver_angles={"B": DriverAngle(0.1)},
-    edge_distances={"AB": 1.0, "BC": 2.0, "CD": 2.0},
+    node_positions={"A": (0, 0), "B": (1, 0), "C": (2, 1), "D": (3, 0)},
+    driver_angles={"B": DriverAngle(0.1)},
+    edge_distances={"AB": 1.0, "BC": 2.0, "CD": 2.0},
 )
 
 # Convert to mechanism for simulation
@@ -1330,13 +1350,13 @@ 
    Module contentsExample
    
-
    >>> topology = HypergraphLinkage(name="leg")
+
    >>> topology = HypergraphLinkage(name="leg")
 >>> # ... add nodes and edges ...
 >>> instance = ComponentInstance(
-...     id="left_leg",
+...     id="left_leg",
 ...     topology=topology,
-...     ports={"input": "A", "output": "B"},
-...     name="Left Leg"
+...     ports={"input": "A", "output": "B"},
+...     name="Left Leg"
 ... )
 
    
 
    
@@ -1412,10 +1432,10 @@ 
    Module contentsExample
    
 
    >>> conn = Connection(
-...     from_instance="leg1",
-...     from_port="output",
-...     to_instance="leg2",
-...     to_port="input"
+...     from_instance="leg1",
+...     from_port="output",
+...     to_instance="leg2",
+...     to_port="input"
 ... )
 
    
 
    
@@ -1459,7 +1479,7 @@ 
    Module contentsExample
    
-
    >>> edge = Edge("AB", source="A", target="B")
+
    >>> edge = Edge("AB", source="A", target="B")
 
    
 
    
 
    
@@ -1527,16 +1547,16 @@ 
    Module contentsExample
    
 
    >>> # Create instances
->>> leg1 = ComponentInstance("leg1", leg_topology, {"input": "A", "output": "B"})
->>> leg2 = ComponentInstance("leg2", leg_topology, {"input": "A", "output": "B"})
+>>> leg1 = ComponentInstance("leg1", leg_topology, {"input": "A", "output": "B"})
+>>> leg2 = ComponentInstance("leg2", leg_topology, {"input": "A", "output": "B"})
 >>>
 >>> # Create hierarchical linkage
 >>> linkage = HierarchicalLinkage(
-...     instances={"leg1": leg1, "leg2": leg2},
+...     instances={"leg1": leg1, "leg2": leg2},
 ...     connections=[
-...         Connection("leg1", "output", "leg2", "input"),
+...         Connection("leg1", "output", "leg2", "input"),
 ...     ],
-...     name="Two-Leg Walker"
+...     name="Two-Leg Walker"
 ... )
 >>>
 >>> # Flatten for simulation
@@ -1640,9 +1660,9 @@ 
    Module contentsExample
    
 
    >>> # Triangle rigid body connecting A, B, C
 >>> he = Hyperedge(
-...     id="triangle",
-...     nodes=("A", "B", "C"),
-...     name="Triangle Link"
+...     id="triangle",
+...     nodes=("A", "B", "C"),
+...     name="Triangle Link"
 ... )
 
    
 
    
@@ -1668,11 +1688,11 @@ 
    Module contentsExample
    
 
    >>> edges = [
-...     Edge("e1", "A", "B"),
-...     Edge("e2", "B", "C"),
+...     Edge("e1", "A", "B"),
+...     Edge("e2", "B", "C"),
 ... ]
->>> he = Hyperedge.from_edges(edges, "combined")
->>> "A" in he.nodes
+>>> he = Hyperedge.from_edges(edges, "combined")
+>>> "A" in he.nodes
 True
 
    
 
    
@@ -1708,7 +1728,7 @@ 
    Module contentsExample
    
-
    >>> he = Hyperedge("tri", ("A", "B", "C"))
+
    >>> he = Hyperedge("tri", ("A", "B", "C"))
 >>> edges = he.to_edges()
 >>> len(edges)
 2
@@ -1751,10 +1771,10 @@ 
    Module contentsExample
    
-
    >>> graph = HypergraphLinkage(name="Four-bar")
->>> graph.add_node(Node("A", role=NodeRole.GROUND))
->>> graph.add_node(Node("B", role=NodeRole.DRIVER))
->>> graph.add_edge(Edge("AB", source="A", target="B"))
+
    >>> graph = HypergraphLinkage(name="Four-bar")
+>>> graph.add_node(Node("A", role=NodeRole.GROUND))
+>>> graph.add_node(Node("B", role=NodeRole.DRIVER))
+>>> graph.add_edge(Edge("AB", source="A", target="B"))
 
    
 
    
 
    
@@ -2091,7 +2111,7 @@ 
    Module contentsExample
    
-
    >>> node = Node("A", role=NodeRole.GROUND)
+
    >>> node = Node("A", role=NodeRole.GROUND)
 >>> node.joint_type
 <JointType.REVOLUTE: 1>
 
    
@@ -2168,6 +2188,11 @@ 
    Module contentsPrismaticJoint keeps its slide line
+as a hyperedge over itself and two ground nodes on the line, the
+encoding to_mechanism() reads. Ground joints that already lie
+on the line are used; otherwise <id>_rail0 / <id>_rail1
+ground nodes are added at line_point and one axis length along.
    
 
    
 
    Parameters:
    
 
    mechanism – The Mechanism to convert.
    
@@ -2327,6 +2352,12 @@ 
    Module contentsJointType.PRISMATIC node is a slider: it needs one
+edge, to the revolute anchor it is linked to, and one hyperedge of
+three nodes whose two other nodes lie on the slide line, which is
+how from_sim_linkage() encodes an RRPDyad. The mechanism
+keeps the line as the PrismaticJoint’s
+axis and line_point, so the two line nodes must be ground.
    
 
    
 
    Parameters:
    
 
    
 
    Raises:
    
-
    ValueError – If the hypergraph is underconstrained or has
-    disconnected components that cannot be solved.
    
+
      
+
    • ValueError – If the hypergraph is underconstrained or has
+    disconnected components that cannot be solved.
      • 
+
    • NotImplementedError – If a prismatic node is not a slider on a
+    fixed line (its guide is a moving link, it has no revolute
+    leg or several, or it is a PPDyad-style double slider),
+    or if a driver node is prismatic (a linear actuator), which
+    Mechanism cannot represent yet.
      • 
+
    
 
    
 
    
 
    Example
    
-
    >>> hg = HypergraphLinkage(name="Four-bar")
->>> hg.add_node(Node("A", role=NodeRole.GROUND))
->>> hg.add_edge(Edge("AB", "A", "B"))
+
    >>> hg = HypergraphLinkage(name="Four-bar")
+>>> hg.add_node(Node("A", role=NodeRole.GROUND))
+>>> hg.add_edge(Edge("AB", "A", "B"))
 >>> dims = Dimensions(
-...     node_positions={"A": (0, 0), "B": (1, 0)},
-...     edge_distances={"AB": 1.0},
+...     node_positions={"A": (0, 0), "B": (1, 0)},
+...     edge_distances={"AB": 1.0},
 ... )
 >>> mechanism = to_mechanism(hg, dims)
 
    
diff --git a/docs/api/pylinkage.linkage.html b/docs/api/pylinkage.linkage.html
index 875fe9b..fb0e890 100644
--- a/docs/api/pylinkage.linkage.html
+++ b/docs/api/pylinkage.linkage.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.linkage package — pylinkage 1.2.2 documentation
+  pylinkage.linkage package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -202,7 +202,10 @@ 
    Submodulespylinkage.linkage.analysis.kinematic_default_test(func: Callable[[...], float], error_penalty: float) → Callable[[Linkage, Iterable[float], JointPositions | None], float]
 
    Standard run for any linkage before a complete fitness evaluation.
    
 
    This decorator makes a kinematic simulation, before passing the loci to the
-decorated function.
    
+decorated function: one complete cycle of the linkage from its initial
+position, at the stride step() uses (dt=1), with at least 96
+frames. An evaluation therefore costs linkage.get_rotation_period()
+steps, the least common multiple of the actuators’ periods.
    
 
    
 
    Parameters:
    
 
    
 
    
@@ -476,11 +479,11 @@ 
    SubmodulesExample
    
 
    >>> tolerances = {
-...     "Crank_radius": 0.1,    # +/- 0.1 mm
-...     "Revolute_dist1": 0.2,  # +/- 0.2 mm
+...     "Crank_radius": 0.1,    # +/- 0.1 mm
+...     "Revolute_dist1": 0.2,  # +/- 0.2 mm
 ... }
 >>> analysis = linkage.tolerance_analysis(tolerances, n_samples=500)
->>> print(f"Max deviation: {analysis.max_deviation:.4f}")
+>>> print(f"Max deviation: {analysis.max_deviation:.4f}")
 >>> analysis.plot_cloud()
 
    
 
    
@@ -1192,7 +1195,7 @@ 
    Module contents
    >>> analysis = linkage.sensitivity_analysis(delta=0.01)
 >>> print(analysis.most_sensitive)
 >>> for name, sens in analysis.sensitivity_ranking:
-...     print(f"{name}: {sens:.4f}")
+...     print(f"{name}: {sens:.4f}")
 
    
 
    
 
    
@@ -1246,11 +1249,11 @@ 
    Module contentsExample
    
 
    >>> tolerances = {
-...     "Crank_radius": 0.1,    # +/- 0.1 mm
-...     "Revolute_dist1": 0.2,  # +/- 0.2 mm
+...     "Crank_radius": 0.1,    # +/- 0.1 mm
+...     "Revolute_dist1": 0.2,  # +/- 0.2 mm
 ... }
 >>> analysis = linkage.tolerance_analysis(tolerances, n_samples=500)
->>> print(f"Max deviation: {analysis.max_deviation:.4f}")
+>>> print(f"Max deviation: {analysis.max_deviation:.4f}")
 >>> analysis.plot_cloud()
 
    
 
    
@@ -1394,7 +1397,10 @@ 
    Module contentspylinkage.linkage.kinematic_default_test(func: Callable[[...], float], error_penalty: float) → Callable[[Linkage, Iterable[float], JointPositions | None], float]
 
    Standard run for any linkage before a complete fitness evaluation.
    
 
    This decorator makes a kinematic simulation, before passing the loci to the
-decorated function.
    
+decorated function: one complete cycle of the linkage from its initial
+position, at the stride step() uses (dt=1), with at least 96
+frames. An evaluation therefore costs linkage.get_rotation_period()
+steps, the least common multiple of the actuators’ periods.
    
 
    
 
    Parameters:
    
 
    
@@ -277,7 +277,7 @@ 
    SubmodulesExample
    
-
    >>> builder.add_ground_link("ground", ports={"O1": (0, 0), "O2": (3, 0)})
+
    >>> builder.add_ground_link("ground", ports={"O1": (0, 0), "O2": (3, 0)})
 
    
 
    
 
    
@@ -300,7 +300,7 @@ 
    SubmodulesExample
    
-
    >>> builder.add_link("coupler", length=2.5)
+
    >>> builder.add_link("coupler", length=2.5)
 
    
 
    
 
    
@@ -330,7 +330,7 @@ 
    SubmodulesExample
    
 
    >>> # Track the midpoint of the coupler link
->>> builder.add_point_tracker("coupler_mid", "coupler.0", "coupler.1")
+>>> builder.add_point_tracker("coupler_mid", "coupler.0", "coupler.1")
 
    
 
    
 
@@ -376,7 +376,7 @@ 
    SubmodulesExample
    
-
    >>> builder.add_slide_axis("rail", through=(0, 0), direction=(1, 0))
+
    >>> builder.add_slide_axis("rail", through=(0, 0), direction=(1, 0))
 
    
 
    
 
@@ -405,8 +405,8 @@ 
    SubmodulesExample
    
 
    >>> builder.add_ternary_link(
-...     "coupler",
-...     port_geometry={"A": (0, 0), "B": (3, 0), "P": (1.5, 1)}
+...     "coupler",
+...     port_geometry={"A": (0, 0), "B": (3, 0), "P": (1.5, 1)}
 ... )
 
    
 
    
@@ -450,7 +450,7 @@ 
    SubmodulesExample
    
-
    >>> builder.connect("crank.tip", "coupler.0")
+
    >>> builder.connect("crank.tip", "coupler.0")
 
    
 
    
 
@@ -473,7 +473,7 @@ 
    SubmodulesExample
    
-
    >>> builder.connect_prismatic("rod.1", "rail")
+
    >>> builder.connect_prismatic("rod.1", "rail")
 
    
 
    
 
@@ -502,7 +502,7 @@ 
    SubmodulesExample
    
-
    >>> builder.set_branch("coupler.1", 1)  # Use "lower" configuration
+
    >>> builder.set_branch("coupler.1", 1)  # Use "lower" configuration
 
    
 
    
 
@@ -840,7 +840,7 @@ 
    SubmodulesExample
    
-
    >>> ground = GroundJoint("O", position=(0.0, 0.0))
+
    >>> ground = GroundJoint("O", position=(0.0, 0.0))
 >>> ground.is_ground
 True
 
    
@@ -1007,7 +1007,7 @@ 
    SubmodulesExample
    
-
    >>> joint = PrismaticJoint("S", position=(0.0, 0.0), axis=(1.0, 0.0))
+
    >>> joint = PrismaticJoint("S", position=(0.0, 0.0), axis=(1.0, 0.0))
 >>> joint.joint_type
 <JointType.PRISMATIC: 2>
 
    
@@ -1050,7 +1050,7 @@ 
    SubmodulesExample
    
-
    >>> joint = RevoluteJoint("A", position=(1.0, 2.0))
+
    >>> joint = RevoluteJoint("A", position=(1.0, 2.0))
 >>> joint.joint_type
 <JointType.REVOLUTE: 1>
 
    
@@ -1087,7 +1087,7 @@ 
    SubmodulesExample
    
 
    >>> # Track the midpoint of a link between joints A and B
->>> tracker = TrackerJoint("midpoint", ref_joint1_id="A", ref_joint2_id="B",
+>>> tracker = TrackerJoint("midpoint", ref_joint1_id="A", ref_joint2_id="B",
 ...                        distance=0.5, angle=0.0)
 
    
 
    
@@ -1167,9 +1167,9 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.mechanism.joint import GroundJoint, RevoluteJoint
->>> O = GroundJoint("O", position=(0.0, 0.0))
->>> A = RevoluteJoint("A", position=(1.0, 0.0))
->>> arc_crank = ArcDriverLink("crank", joints=[O, A], motor_joint=O,
+>>> O = GroundJoint("O", position=(0.0, 0.0))
+>>> A = RevoluteJoint("A", position=(1.0, 0.0))
+>>> arc_crank = ArcDriverLink("crank", joints=[O, A], motor_joint=O,
 ...                           angular_velocity=0.1,
 ...                           arc_start=0.5, arc_end=2.5)
 
    
@@ -1222,6 +1222,14 @@ 
    Submodules
+
    
+read_angle() → None
    
+
    Set current_angle from where the motor and output joints are.
    
+
    The angle is brought onto the arc and the sweep restarts in the
+positive direction, as on a new crank.
    
+
    
+
 
    
 
    
 reset() → None
    
@@ -1263,9 +1271,9 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.mechanism.joint import GroundJoint, RevoluteJoint
->>> O = GroundJoint("O", position=(0.0, 0.0))
->>> A = RevoluteJoint("A", position=(1.0, 0.0))
->>> crank = DriverLink("crank", joints=[O, A], motor_joint=O,
+>>> O = GroundJoint("O", position=(0.0, 0.0))
+>>> A = RevoluteJoint("A", position=(1.0, 0.0))
+>>> crank = DriverLink("crank", joints=[O, A], motor_joint=O,
 ...                    angular_velocity=0.1)
 
    
 
    
@@ -1309,6 +1317,14 @@ 
    Submodules
+
    
+read_angle() → None
    
+
    Set current_angle from where the motor and output joints are.
    
+
    The crank is then in the state its joints describe, so putting
+a mechanism back in a position puts its drivers back too.
    
+
    
+
 
    
 
    
 reset() → None
    
@@ -1344,9 +1360,9 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.mechanism.joint import GroundJoint
->>> O1 = GroundJoint("O1", position=(0.0, 0.0))
->>> O2 = GroundJoint("O2", position=(2.0, 0.0))
->>> ground = GroundLink("ground", joints=[O1, O2])
+>>> O1 = GroundJoint("O1", position=(0.0, 0.0))
+>>> O2 = GroundJoint("O2", position=(2.0, 0.0))
+>>> ground = GroundLink("ground", joints=[O1, O2])
 
    
 
    
 
    
@@ -1381,9 +1397,9 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.mechanism.joint import RevoluteJoint
->>> j1 = RevoluteJoint("A", position=(0.0, 0.0))
->>> j2 = RevoluteJoint("B", position=(1.0, 0.0))
->>> link = Link("AB", joints=[j1, j2])
+>>> j1 = RevoluteJoint("A", position=(0.0, 0.0))
+>>> j2 = RevoluteJoint("B", position=(1.0, 0.0))
+>>> link = Link("AB", joints=[j1, j2])
 >>> link.length
 1.0
 
    
@@ -1568,12 +1584,12 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.mechanism import Mechanism, GroundJoint, create_crank, create_rrr_dyad
 >>> # Create a four-bar linkage
->>> O1 = GroundJoint("O1", position=(0.0, 0.0))
->>> O2 = GroundJoint("O2", position=(2.0, 0.0))
->>> ground = GroundLink("ground", joints=[O1, O2])
+>>> O1 = GroundJoint("O1", position=(0.0, 0.0))
+>>> O2 = GroundJoint("O2", position=(2.0, 0.0))
+>>> ground = GroundLink("ground", joints=[O1, O2])
 >>> crank, A = create_crank(O1, radius=1.0, angular_velocity=0.1)
 >>> link1, link2, B = create_rrr_dyad(A, O2, distance1=2.0, distance2=1.5)
->>> mechanism = Mechanism("Four-Bar", joints=[O1, O2, A, B],
+>>> mechanism = Mechanism("Four-Bar", joints=[O1, O2, A, B],
 ...                       links=[ground, crank, link1, link2])
 
    
 
    
@@ -1678,8 +1694,12 @@ 
    Submodules3·(n − 1) − 2·R − P where n is the total number
 of links (including the ground frame), R counts revolute
-pairs (RevoluteJoint and GroundJoint) and P counts
-prismatic pairs.
    
+pairs and P prismatic pairs. A joint on k links joins
+them with k − 1 pairs: a ground joint that only marks a
+point of the frame, or a coupler point, is no pair at all. A
+PrismaticJoint adds the prismatic pair with the frame its
+slide line stands for, on top of the revolute pairs of its
+links.
    
 
    Positive ⇒ unconstrained DOF (a 1-DOF four-bar returns 1);
 zero ⇒ statically determinate; negative ⇒ over-constrained.
    
 
    
@@ -1776,7 +1796,7 @@ 
    Submodules
 
    
 set_joint_positions(positions: list[Coord]) → None
    
-
    Set positions of all joints.
    
+
    Set positions of all joints, and read the drivers’ angles from them.
    
 
    
 
 
    
@@ -2051,9 +2071,9 @@ 
    Module contents... )
 >>>
 >>> # Create ground joints
->>> O1 = GroundJoint("O1", position=(0.0, 0.0))
->>> O2 = GroundJoint("O2", position=(2.0, 0.0))
->>> ground = GroundLink("ground", joints=[O1, O2])
+>>> O1 = GroundJoint("O1", position=(0.0, 0.0))
+>>> O2 = GroundJoint("O2", position=(2.0, 0.0))
+>>> ground = GroundLink("ground", joints=[O1, O2])
 
    
 
    
 
@@ -2101,9 +2121,9 @@ 
    Module contentsExample
    
 
    >>> from pylinkage.mechanism.joint import GroundJoint, RevoluteJoint
->>> O = GroundJoint("O", position=(0.0, 0.0))
->>> A = RevoluteJoint("A", position=(1.0, 0.0))
->>> arc_crank = ArcDriverLink("crank", joints=[O, A], motor_joint=O,
+>>> O = GroundJoint("O", position=(0.0, 0.0))
+>>> A = RevoluteJoint("A", position=(1.0, 0.0))
+>>> arc_crank = ArcDriverLink("crank", joints=[O, A], motor_joint=O,
 ...                           angular_velocity=0.1,
 ...                           arc_start=0.5, arc_end=2.5)
 
    
@@ -2156,6 +2176,14 @@ 
    Module contents
+
    
+read_angle() → None
    
+
    Set current_angle from where the motor and output joints are.
    
+
    The angle is brought onto the arc and the sweep restarts in the
+positive direction, as on a new crank.
    
+
    
+
 
    
 
    
 reset() → None
    
@@ -2197,9 +2225,9 @@ 
    Module contentsExample
    
 
    >>> from pylinkage.mechanism.joint import GroundJoint, RevoluteJoint
->>> O = GroundJoint("O", position=(0.0, 0.0))
->>> A = RevoluteJoint("A", position=(1.0, 0.0))
->>> crank = DriverLink("crank", joints=[O, A], motor_joint=O,
+>>> O = GroundJoint("O", position=(0.0, 0.0))
+>>> A = RevoluteJoint("A", position=(1.0, 0.0))
+>>> crank = DriverLink("crank", joints=[O, A], motor_joint=O,
 ...                    angular_velocity=0.1)
 
    
 
    
@@ -2243,6 +2271,14 @@ 
    Module contents
+
    
+read_angle() → None
    
+
    Set current_angle from where the motor and output joints are.
    
+
    The crank is then in the state its joints describe, so putting
+a mechanism back in a position puts its drivers back too.
    
+
    
+
 
    
 
    
 reset() → None
    
@@ -2277,7 +2313,7 @@ 
    Module contentsExample
    
-
    >>> ground = GroundJoint("O", position=(0.0, 0.0))
+
    >>> ground = GroundJoint("O", position=(0.0, 0.0))
 >>> ground.is_ground
 True
 
    
@@ -2309,9 +2345,9 @@ 
    Module contentsExample
    
 
    >>> from pylinkage.mechanism.joint import GroundJoint
->>> O1 = GroundJoint("O1", position=(0.0, 0.0))
->>> O2 = GroundJoint("O2", position=(2.0, 0.0))
->>> ground = GroundLink("ground", joints=[O1, O2])
+>>> O1 = GroundJoint("O1", position=(0.0, 0.0))
+>>> O2 = GroundJoint("O2", position=(2.0, 0.0))
+>>> ground = GroundLink("ground", joints=[O1, O2])
 
    
 
    
 
    
@@ -2475,9 +2511,9 @@ 
    Module contentsExample
    
 
    >>> from pylinkage.mechanism.joint import RevoluteJoint
->>> j1 = RevoluteJoint("A", position=(0.0, 0.0))
->>> j2 = RevoluteJoint("B", position=(1.0, 0.0))
->>> link = Link("AB", joints=[j1, j2])
+>>> j1 = RevoluteJoint("A", position=(0.0, 0.0))
+>>> j2 = RevoluteJoint("B", position=(1.0, 0.0))
+>>> link = Link("AB", joints=[j1, j2])
 >>> link.length
 1.0
 
    
@@ -2648,12 +2684,12 @@ 
    Module contentsExample
    
 
    >>> from pylinkage.mechanism import Mechanism, GroundJoint, create_crank, create_rrr_dyad
 >>> # Create a four-bar linkage
->>> O1 = GroundJoint("O1", position=(0.0, 0.0))
->>> O2 = GroundJoint("O2", position=(2.0, 0.0))
->>> ground = GroundLink("ground", joints=[O1, O2])
+>>> O1 = GroundJoint("O1", position=(0.0, 0.0))
+>>> O2 = GroundJoint("O2", position=(2.0, 0.0))
+>>> ground = GroundLink("ground", joints=[O1, O2])
 >>> crank, A = create_crank(O1, radius=1.0, angular_velocity=0.1)
 >>> link1, link2, B = create_rrr_dyad(A, O2, distance1=2.0, distance2=1.5)
->>> mechanism = Mechanism("Four-Bar", joints=[O1, O2, A, B],
+>>> mechanism = Mechanism("Four-Bar", joints=[O1, O2, A, B],
 ...                       links=[ground, crank, link1, link2])
 
    
 
    
@@ -2758,8 +2794,12 @@ 
    Module contents3·(n − 1) − 2·R − P where n is the total number
 of links (including the ground frame), R counts revolute
-pairs (RevoluteJoint and GroundJoint) and P counts
-prismatic pairs.
    
+pairs and P prismatic pairs. A joint on k links joins
+them with k − 1 pairs: a ground joint that only marks a
+point of the frame, or a coupler point, is no pair at all. A
+PrismaticJoint adds the prismatic pair with the frame its
+slide line stands for, on top of the revolute pairs of its
+links.
    
 
    Positive ⇒ unconstrained DOF (a 1-DOF four-bar returns 1);
 zero ⇒ statically determinate; negative ⇒ over-constrained.
    
 
    
@@ -2856,7 +2896,7 @@ 
    Module contents
 
    
 set_joint_positions(positions: list[Coord]) → None
    
-
    Set positions of all joints.
    
+
    Set positions of all joints, and read the drivers’ angles from them.
    
 
    
 
 
    
@@ -2972,14 +3012,14 @@ 
    Module contentsExample
    
-
    >>> builder = MechanismBuilder("four-bar")
->>> builder.add_ground_link("ground", ports={"O1": (0, 0), "O2": (3, 0)})
->>> builder.add_driver_link("crank", length=1.0, motor_port="O1")
->>> builder.add_link("coupler", length=2.5)
->>> builder.add_link("rocker", length=1.5)
->>> builder.connect("crank.tip", "coupler.0")
->>> builder.connect("coupler.1", "rocker.0")
->>> builder.connect("rocker.1", "ground.O2")
+
    >>> builder = MechanismBuilder("four-bar")
+>>> builder.add_ground_link("ground", ports={"O1": (0, 0), "O2": (3, 0)})
+>>> builder.add_driver_link("crank", length=1.0, motor_port="O1")
+>>> builder.add_link("coupler", length=2.5)
+>>> builder.add_link("rocker", length=1.5)
+>>> builder.connect("crank.tip", "coupler.0")
+>>> builder.connect("coupler.1", "rocker.0")
+>>> builder.connect("rocker.1", "ground.O2")
 >>> mechanism = builder.build()
 
    
 
    
@@ -3008,7 +3048,7 @@ 
    Module contentsExample
    
-
    >>> builder.add_arc_driver_link("crank", length=1.0, motor_port="O1",
+
    >>> builder.add_arc_driver_link("crank", length=1.0, motor_port="O1",
 ...                             arc_start=0.5, arc_end=2.5)
 
    
 
    
@@ -3036,7 +3076,7 @@ 
    Module contentsExample
    
-
    >>> builder.add_driver_link("crank", length=1.0, motor_port="O1", omega=0.1)
+
    >>> builder.add_driver_link("crank", length=1.0, motor_port="O1", omega=0.1)
 
    
 
    
 
    
@@ -3060,7 +3100,7 @@ 
    Module contentsExample
    
-
    >>> builder.add_ground_link("ground", ports={"O1": (0, 0), "O2": (3, 0)})
+
    >>> builder.add_ground_link("ground", ports={"O1": (0, 0), "O2": (3, 0)})
 
    
 
    
 
@@ -3083,7 +3123,7 @@ 
    Module contentsExample
    
-
    >>> builder.add_link("coupler", length=2.5)
+
    >>> builder.add_link("coupler", length=2.5)
 
    
 
    
 
@@ -3113,7 +3153,7 @@ 
    Module contentsExample
    
 
    >>> # Track the midpoint of the coupler link
->>> builder.add_point_tracker("coupler_mid", "coupler.0", "coupler.1")
+>>> builder.add_point_tracker("coupler_mid", "coupler.0", "coupler.1")
 
    
 
    
 
@@ -3159,7 +3199,7 @@ 
    Module contentsExample
    
-
    >>> builder.add_slide_axis("rail", through=(0, 0), direction=(1, 0))
+
    >>> builder.add_slide_axis("rail", through=(0, 0), direction=(1, 0))
 
    
 
    
 
@@ -3188,8 +3228,8 @@ 
    Module contentsExample
    
 
    >>> builder.add_ternary_link(
-...     "coupler",
-...     port_geometry={"A": (0, 0), "B": (3, 0), "P": (1.5, 1)}
+...     "coupler",
+...     port_geometry={"A": (0, 0), "B": (3, 0), "P": (1.5, 1)}
 ... )
 
    
 
    
@@ -3233,7 +3273,7 @@ 
    Module contentsExample
    
-
    >>> builder.connect("crank.tip", "coupler.0")
+
    >>> builder.connect("crank.tip", "coupler.0")
 
    
 
    
 
@@ -3256,7 +3296,7 @@ 
    Module contentsExample
    
-
    >>> builder.connect_prismatic("rod.1", "rail")
+
    >>> builder.connect_prismatic("rod.1", "rail")
 
    
 
    
 
@@ -3285,7 +3325,7 @@ 
    Module contentsExample
    
-
    >>> builder.set_branch("coupler.1", 1)  # Use "lower" configuration
+
    >>> builder.set_branch("coupler.1", 1)  # Use "lower" configuration
 
    
 
    
 
@@ -3312,7 +3352,7 @@ 
    Module contentsExample
    
-
    >>> joint = PrismaticJoint("S", position=(0.0, 0.0), axis=(1.0, 0.0))
+
    >>> joint = PrismaticJoint("S", position=(0.0, 0.0), axis=(1.0, 0.0))
 >>> joint.joint_type
 <JointType.PRISMATIC: 2>
 
    
@@ -3355,7 +3395,7 @@ 
    Module contentsExample
    
-
    >>> joint = RevoluteJoint("A", position=(1.0, 2.0))
+
    >>> joint = RevoluteJoint("A", position=(1.0, 2.0))
 >>> joint.joint_type
 <JointType.REVOLUTE: 1>
 
    
@@ -3392,7 +3432,7 @@ 
    Module contentsExample
    
 
    >>> # Track the midpoint of a link between joints A and B
->>> tracker = TrackerJoint("midpoint", ref_joint1_id="A", ref_joint2_id="B",
+>>> tracker = TrackerJoint("midpoint", ref_joint1_id="A", ref_joint2_id="B",
 ...                        distance=0.5, angle=0.0)
 
    
 
    
diff --git a/docs/api/pylinkage.optimization.collections.html b/docs/api/pylinkage.optimization.collections.html
index 052b2ce..6335b0f 100644
--- a/docs/api/pylinkage.optimization.collections.html
+++ b/docs/api/pylinkage.optimization.collections.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.optimization.collections package — pylinkage 1.2.2 documentation
+  pylinkage.optimization.collections package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/api/pylinkage.optimization.html b/docs/api/pylinkage.optimization.html
index c7c61dc..1b3cb16 100644
--- a/docs/api/pylinkage.optimization.html
+++ b/docs/api/pylinkage.optimization.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.optimization package — pylinkage 1.2.2 documentation
+  pylinkage.optimization package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -364,7 +364,7 @@ 
    Submodules
    async def my_optimization():
     def progress_handler(progress):
-        print(f"Progress: {progress.progress_fraction:.1%}")
+        print(f"Progress: {progress.progress_fraction:.1%}")
 
     results = await particle_swarm_optimization_async(
         eval_func=my_fitness,
@@ -417,7 +417,7 @@ 
    Submodules
    async def my_optimization():
     def progress_handler(progress):
-        print(f"Progress: {progress.progress_fraction:.1%}")
+        print(f"Progress: {progress.progress_fraction:.1%}")
 
     results = await trials_and_errors_optimization_async(
         eval_func=my_fitness,
@@ -741,9 +741,9 @@ 
    Submodulesresult = co_optimize(
     objectives=[accuracy_obj, compactness_obj],
     precision_points=points,
-    objective_names=["Path Error", "Compactness"],
+    objective_names=["Path Error", "Compactness"],
 )
-print(f"Found {len(result.pareto_front)} Pareto solutions")
+print(f"Found {len(result.pareto_front)} Pareto solutions")
 
    
 
    
 
    
@@ -876,7 +876,7 @@ 
    Submodulespareto = multi_objective_optimization(
     objectives=[path_error, transmission_penalty],
     linkage=my_linkage,
-    objective_names=["Path Error", "Transmission Penalty"],
+    objective_names=["Path Error", "Transmission Penalty"],
     n_generations=100,
 )
 
@@ -1047,8 +1047,8 @@ 
    Submoduleseval_func=fitness,
     linkage=my_linkage,
     stages=[
-        (differential_evolution_optimization, {"maxiter": 300}),
-        (minimize_linkage, {"method": "Nelder-Mead", "maxiter": 500}),
+        (differential_evolution_optimization, {"maxiter": 300}),
+        (minimize_linkage, {"method": "Nelder-Mead", "maxiter": 500}),
     ],
     order_relation=min,
 )
@@ -1232,7 +1232,7 @@ 
    Submoduleseval_func=fitness,
     linkage=my_linkage,
     x0=initial_guess,
-    method="Nelder-Mead",
+    method="Nelder-Mead",
     order_relation=min,
 )
 best = result[0]  # Member with .score, .dimensions, .initial_positions
@@ -1419,7 +1419,7 @@ 
    Submodulesresult = warm_start_co_optimization(
     precision_points=points,
     objectives=[accuracy],
-    objective_names=["Path Error"],
+    objective_names=["Path Error"],
 )
 
    
 
    
diff --git a/docs/api/pylinkage.population.html b/docs/api/pylinkage.population.html
index 27e2858..b32ea38 100644
--- a/docs/api/pylinkage.population.html
+++ b/docs/api/pylinkage.population.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.population package — pylinkage 1.2.2 documentation
+  pylinkage.population package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/api/pylinkage.simulation.html b/docs/api/pylinkage.simulation.html
index 0036a82..ff98675 100644
--- a/docs/api/pylinkage.simulation.html
+++ b/docs/api/pylinkage.simulation.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.simulation package — pylinkage 1.2.2 documentation
+  pylinkage.simulation package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -146,11 +146,11 @@ 
    Submodules>>> from pylinkage.dyads import RRRDyad
 >>> from pylinkage.simulation import Linkage
 >>>
->>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0, angular_velocity=0.1)
 >>> rocker = RRRDyad(crank.output, O2, distance1=2.0, distance2=1.5)
->>> linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
+>>> linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
 >>> for positions in linkage.step():
 ...     print(positions)
 
    
@@ -358,7 +358,7 @@ 
    SubmodulesExample
    
 
    >>> linkage.set_input_velocity(crank, omega=10.0)  # 10 rad/s
 >>> for pos, vel, acc in linkage.step_with_derivatives():
-...     print(f"Position: {pos}, Velocity: {vel}")
+...     print(f"Position: {pos}, Velocity: {vel}")
 
    
 
    
 
@@ -457,7 +457,7 @@ 
    SubmodulesExample
    
 
    >>> linkage.set_input_velocity(crank, omega=10.0)
 >>> for pos, vel, acc in linkage.step_with_derivatives():
-...     print(f"Crank velocity: {vel[2]}")
+...     print(f"Crank velocity: {vel[2]}")
 
    
 
    
 
@@ -503,8 +503,8 @@ 
    Module contentsfrom pylinkage.simulation import Linkage
 
 # Ground points
-O1 = Ground(0.0, 0.0, name="O1")
-O2 = Ground(2.0, 0.0, name="O2")
+O1 = Ground(0.0, 0.0, name="O1")
+O2 = Ground(2.0, 0.0, name="O2")
 
 # Crank (driver)
 crank = Crank(anchor=O1, radius=1.0, angular_velocity=0.1)
@@ -518,7 +518,7 @@ 
    Module contents)
 
 # Build and simulate
-linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
+linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
 for positions in linkage.step():
     print(positions)
 
    
@@ -537,11 +537,11 @@ 
    Module contents>>> from pylinkage.dyads import RRRDyad
 >>> from pylinkage.simulation import Linkage
 >>>
->>> O1 = Ground(0.0, 0.0, name="O1")
->>> O2 = Ground(2.0, 0.0, name="O2")
+>>> O1 = Ground(0.0, 0.0, name="O1")
+>>> O2 = Ground(2.0, 0.0, name="O2")
 >>> crank = Crank(anchor=O1, radius=1.0, angular_velocity=0.1)
 >>> rocker = RRRDyad(crank.output, O2, distance1=2.0, distance2=1.5)
->>> linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
+>>> linkage = Linkage([O1, O2, crank, rocker], name="Four-Bar")
 >>> for positions in linkage.step():
 ...     print(positions)
 
    
@@ -749,7 +749,7 @@ 
    Module contentsExample
    
 
    >>> linkage.set_input_velocity(crank, omega=10.0)  # 10 rad/s
 >>> for pos, vel, acc in linkage.step_with_derivatives():
-...     print(f"Position: {pos}, Velocity: {vel}")
+...     print(f"Position: {pos}, Velocity: {vel}")
 
    
 
    
 
@@ -848,7 +848,7 @@ 
    Module contentsExample
    
 
    >>> linkage.set_input_velocity(crank, omega=10.0)
 >>> for pos, vel, acc in linkage.step_with_derivatives():
-...     print(f"Crank velocity: {vel[2]}")
+...     print(f"Crank velocity: {vel[2]}")
 
    
 
    
 
diff --git a/docs/api/pylinkage.solver.html b/docs/api/pylinkage.solver.html
index 2ac4ff2..ca2bf4a 100644
--- a/docs/api/pylinkage.solver.html
+++ b/docs/api/pylinkage.solver.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.solver package — pylinkage 1.2.2 documentation
+  pylinkage.solver package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/api/pylinkage.symbolic.html b/docs/api/pylinkage.symbolic.html
index 1409d36..ecd9262 100644
--- a/docs/api/pylinkage.symbolic.html
+++ b/docs/api/pylinkage.symbolic.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.symbolic package — pylinkage 1.2.2 documentation
+  pylinkage.symbolic package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -708,13 +708,13 @@ 
    SubmodulesExample
    
 
    >>> def objective(trajectories):
-...     x, y = trajectories["C"]
+...     x, y = trajectories["C"]
 ...     return (y - 2)**2  # Minimize deviation from y=2
 ...
 >>> optimizer = SymbolicOptimizer(linkage, objective)
 >>> result = optimizer.optimize(
-...     initial_params={"r_AB": 1.0, "r_BC": 3.0, "r_CD": 3.0},
-...     bounds={"r_AB": (0.5, 2), "r_BC": (1, 5), "r_CD": (1, 5)},
+...     initial_params={"r_AB": 1.0, "r_BC": 3.0, "r_CD": 3.0},
+...     bounds={"r_AB": (0.5, 2), "r_BC": (1, 5), "r_CD": (1, 5)},
 ... )
 
    
 
    
@@ -863,9 +863,9 @@ 
    SubmodulesExample
    
-
    >>> buildable, msg = check_buildability(linkage, {"r0": 1, "r1": 10})
+
    >>> buildable, msg = check_buildability(linkage, {"r0": 1, "r1": 10})
 >>> if not buildable:
-...     print(f"Linkage is unbuildable: {msg}")
+...     print(f"Linkage is unbuildable: {msg}")
 
    
 
    
 
@@ -910,7 +910,7 @@ 
    SubmodulesExample
    
 
    >>> funcs = create_trajectory_functions(linkage)
->>> x_func, y_func, params = funcs["C"]
+>>> x_func, y_func, params = funcs["C"]
 >>> x_vals = x_func(theta_array, *[param_values[str(p)] for p in params])
 
    
 
    
@@ -924,8 +924,12 @@ 
    Submodulessqrt(R) of the
+parametrization becomes a symbol r with the constraint
+r^2 = R, so the system is polynomial; a Groebner basis then
+eliminates c, s and every r. The curve found is the full algebraic
+curve: both signs of every root, hence both assembly branches of the
+joint, lie on it.
    
 
    
 
    Parameters:
    
 
    
+
    
+
    Note
    
+
    The joint at the end of the first dyad has a single square root
+in its parametrization and its curve comes out in a fraction of a
+second. A joint built on that one has a root inside a root, and
+the Groebner basis computation may then run for minutes.
    
+
    
 
    Example
    
-
    >>> theta = sp.Symbol('theta')
+
    >>> theta = sp.Symbol('theta')
 >>> x = sp.cos(theta)
 >>> y = sp.sin(theta)
 >>> eliminate_theta(x, y, theta)
@@ -994,23 +1007,23 @@ 
    Module contents# Create a four-bar linkage symbolically
 linkage = fourbar_symbolic(
     ground_length=4,
-    crank_length="L1",  # Symbolic parameter
-    coupler_length="L2",
-    rocker_length="L3",
+    crank_length="L1",  # Symbolic parameter
+    coupler_length="L2",
+    rocker_length="L3",
 )
 
 # Get closed-form trajectory expression for coupler point C
-x_expr, y_expr = linkage.coupler_curve("C")
-print(f"C_x(theta) = {x_expr}")
-print(f"C_y(theta) = {y_expr}")
+x_expr, y_expr = linkage.coupler_curve("C")
+print(f"C_x(theta) = {x_expr}")
+print(f"C_y(theta) = {y_expr}")
 
 # Compute numeric trajectory with specific parameter values
-params = {"L1": 1.0, "L2": 3.0, "L3": 3.0}
+params = {"L1": 1.0, "L2": 3.0, "L3": 3.0}
 theta_vals = np.linspace(0, 2 * np.pi, 360)
 trajectories = compute_trajectory_numeric(linkage, params, theta_vals)
 
 # Access (x, y) positions for joint C
-C_positions = trajectories["C"]  # Shape: (360, 2)
+C_positions = trajectories["C"]  # Shape: (360, 2)
 
    
 
    
 
    For optimization:
    
@@ -1018,19 +1031,19 @@ 
    Module contents# Define objective function symbolically
 def objective(trajectories):
-    x, y = trajectories["C"]
+    x, y = trajectories["C"]
     # Minimize deviation from target y=2
     return (y - 2)**2
 
 optimizer = SymbolicOptimizer(linkage, objective)
 result = optimizer.optimize(
-    initial_params={"L1": 1.0, "L2": 3.0, "L3": 3.0},
-    bounds={"L1": (0.5, 2), "L2": (1, 5), "L3": (1, 5)},
+    initial_params={"L1": 1.0, "L2": 3.0, "L3": 3.0},
+    bounds={"L1": (0.5, 2), "L2": (1, 5), "L3": (1, 5)},
 )
 
 if result.success:
-    print(f"Optimal parameters: {result.params}")
-    print(f"Objective value: {result.objective_value}")
+    print(f"Optimal parameters: {result.params}")
+    print(f"Objective value: {result.objective_value}")
 
    
 
    
 
    
@@ -1410,13 +1423,13 @@ 
    Module contentsExample
    
 
    >>> def objective(trajectories):
-...     x, y = trajectories["C"]
+...     x, y = trajectories["C"]
 ...     return (y - 2)**2  # Minimize deviation from y=2
 ...
 >>> optimizer = SymbolicOptimizer(linkage, objective)
 >>> result = optimizer.optimize(
-...     initial_params={"r_AB": 1.0, "r_BC": 3.0, "r_CD": 3.0},
-...     bounds={"r_AB": (0.5, 2), "r_BC": (1, 5), "r_CD": (1, 5)},
+...     initial_params={"r_AB": 1.0, "r_BC": 3.0, "r_CD": 3.0},
+...     bounds={"r_AB": (0.5, 2), "r_BC": (1, 5), "r_CD": (1, 5)},
 ... )
 
    
 
    
@@ -1504,9 +1517,9 @@ 
    Module contentsExample
    
-
    >>> buildable, msg = check_buildability(linkage, {"r0": 1, "r1": 10})
+
    >>> buildable, msg = check_buildability(linkage, {"r0": 1, "r1": 10})
 >>> if not buildable:
-...     print(f"Linkage is unbuildable: {msg}")
+...     print(f"Linkage is unbuildable: {msg}")
 
    
 
    
 
    
@@ -1551,7 +1564,7 @@ 
    Module contentsExample
    
 
    >>> funcs = create_trajectory_functions(linkage)
->>> x_func, y_func, params = funcs["C"]
+>>> x_func, y_func, params = funcs["C"]
 >>> x_vals = x_func(theta_array, *[param_values[str(p)] for p in params])
 
    
 
    
@@ -1565,8 +1578,12 @@ 
    Module contentssqrt(R) of the
+parametrization becomes a symbol r with the constraint
+r^2 = R, so the system is polynomial; a Groebner basis then
+eliminates c, s and every r. The curve found is the full algebraic
+curve: both signs of every root, hence both assembly branches of the
+joint, lie on it.
    
 
    
 
    Parameters:
    
 
    
+
    
+
    Note
    
+
    The joint at the end of the first dyad has a single square root
+in its parametrization and its curve comes out in a fraction of a
+second. A joint built on that one has a root inside a root, and
+the Groebner basis computation may then run for minutes.
    
+
    
 
    Example
    
-
    >>> theta = sp.Symbol('theta')
+
    >>> theta = sp.Symbol('theta')
 >>> x = sp.cos(theta)
 >>> y = sp.sin(theta)
 >>> eliminate_theta(x, y, theta)
diff --git a/docs/api/pylinkage.synthesis.html b/docs/api/pylinkage.synthesis.html
index eb62219..c6deb00 100644
--- a/docs/api/pylinkage.synthesis.html
+++ b/docs/api/pylinkage.synthesis.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.synthesis package — pylinkage 1.2.2 documentation
+  pylinkage.synthesis package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -954,7 +954,7 @@ 
    Submodules
    >>> pairs = [(0, 0), (math.pi/6, math.pi/4), (math.pi/3, math.pi/2)]
 >>> result = function_generation(pairs)
 >>> for linkage in result.solutions:
-...     print(f"Crank: {linkage.joints[2].r:.3f}")
+...     print(f"Crank: {linkage.joints[2].r:.3f}")
 
    
 
    
 
@@ -1114,7 +1114,7 @@ 
    Submodules...     Pose(2, 0.5, 1.0),
 ... ]
 >>> result = motion_generation(poses)
->>> print(f"Found {len(result.solutions)} solutions")
+>>> print(f"Found {len(result.solutions)} solutions")
 
    
 
    
 
@@ -1154,7 +1154,7 @@ 
    Submodulessolutions = synthesize(points, max_links=6)
 
 for sol in solutions[:3]:
-    print(f"{sol.topology_entry.name}: score={sol.metrics.overall_score:.3f}")
+    print(f"{sol.topology_entry.name}: score={sol.metrics.overall_score:.3f}")
     sol.linkage.show()
 
    
 
    
@@ -1217,7 +1217,7 @@ 
    SubmodulesExample
    
 
    >>> solutions = synthesize([(0,1), (1,2), (2,1.5), (3,0), (4,1)])
->>> print(f"Best: {solutions[0].topology_entry.name}")
+>>> print(f"Best: {solutions[0].topology_entry.name}")
 
    
 
    
 
@@ -1311,7 +1311,7 @@ 
    SubmodulesExample
    
 
    >>> points = [(0, 1), (1, 2), (2, 1.5), (3, 0)]
 >>> result = path_generation(points)
->>> print(f"Found {len(result.solutions)} solutions")
+>>> print(f"Found {len(result.solutions)} solutions")
 >>> for linkage in result.solutions:
 ...     linkage.show()
 
    
@@ -1547,8 +1547,8 @@ 
    SubmodulesExample
    
 
    >>> points = [(0, 0), (1, 2), (2, 3), (3, 2), (4, 0)]
->>> result = six_bar_path_generation(points, topology="watt")
->>> print(f"Found {len(result.solutions)} solutions")
+>>> result = six_bar_path_generation(points, topology="watt")
+>>> print(f"Found {len(result.solutions)} solutions")
 
    
 
    
 
@@ -2120,7 +2120,7 @@ 
    Quick Startprecision_points = [(0, 1), (1, 2), (2, 1.5), (3, 0)]
 result = path_generation(precision_points)
 
-print(f"Found {len(result.solutions)} solutions")
+print(f"Found {len(result.solutions)} solutions")
 for linkage in result.solutions:
     linkage.show()
 
    
@@ -2139,7 +2139,7 @@ 
    Quick Startif result.solutions:
     linkage = result.solutions[0]
-    print(f"Crank length: {linkage.joints[2].r:.3f}")
+    print(f"Crank length: {linkage.joints[2].r:.3f}")
 
    
 
    
 
    Motion Generation:
    
@@ -2162,7 +2162,7 @@ 
    Working with Results# Check if solutions were found
 if result.solutions:
-    print(f"Found {len(result.solutions)} solutions")
+    print(f"Found {len(result.solutions)} solutions")
 
 # Iterate over solutions
 for linkage in result.solutions:
@@ -2170,11 +2170,11 @@ 
    Working with Results# Access warnings
 for warning in result.warnings:
-    print(f"Warning: {warning}")
+    print(f"Warning: {warning}")
 
 # Access raw mathematical solutions
 for sol in result.raw_solutions:
-    print(f"Crank: {sol.crank_length:.3f}")
+    print(f"Crank: {sol.crank_length:.3f}")
 
    
 
    
 
@@ -3178,7 +3178,7 @@ 
    Synthesis Theory Overview
    >>> pairs = [(0, 0), (math.pi/6, math.pi/4), (math.pi/3, math.pi/2)]
 >>> result = function_generation(pairs)
 >>> for linkage in result.solutions:
-...     print(f"Crank: {linkage.joints[2].r:.3f}")
+...     print(f"Crank: {linkage.joints[2].r:.3f}")
 
    
 
    
 
@@ -3326,7 +3326,7 @@ 
    Synthesis Theory Overview...     Pose(2, 0.5, 1.0),
 ... ]
 >>> result = motion_generation(poses)
->>> print(f"Found {len(result.solutions)} solutions")
+>>> print(f"Found {len(result.solutions)} solutions")
 
    
 
    
 
@@ -3382,7 +3382,7 @@ 
    Synthesis Theory OverviewExample
    
 
    >>> solutions = synthesize([(0,1), (1,2), (2,1.5), (3,0), (4,1)])
->>> print(f"Best: {solutions[0].topology_entry.name}")
+>>> print(f"Best: {solutions[0].topology_entry.name}")
 
    
 
    
 
@@ -3459,7 +3459,7 @@ 
    Synthesis Theory OverviewExample
    
 
    >>> points = [(0, 1), (1, 2), (2, 1.5), (3, 0)]
 >>> result = path_generation(points)
->>> print(f"Found {len(result.solutions)} solutions")
+>>> print(f"Found {len(result.solutions)} solutions")
 >>> for linkage in result.solutions:
 ...     linkage.show()
 
    
@@ -3555,8 +3555,8 @@ 
    Synthesis Theory OverviewExample
    
 
    >>> points = [(0, 0), (1, 2), (2, 3), (3, 2), (4, 0)]
->>> result = six_bar_path_generation(points, topology="watt")
->>> print(f"Found {len(result.solutions)} solutions")
+>>> result = six_bar_path_generation(points, topology="watt")
+>>> print(f"Found {len(result.solutions)} solutions")
 
    
 
    
 
diff --git a/docs/api/pylinkage.topology.data.html b/docs/api/pylinkage.topology.data.html
index 2223870..8cb4d03 100644
--- a/docs/api/pylinkage.topology.data.html
+++ b/docs/api/pylinkage.topology.data.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.topology.data package — pylinkage 1.2.2 documentation
+  pylinkage.topology.data package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/api/pylinkage.topology.html b/docs/api/pylinkage.topology.html
index 7ee6bd2..61e95c9 100644
--- a/docs/api/pylinkage.topology.html
+++ b/docs/api/pylinkage.topology.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.topology package — pylinkage 1.2.2 documentation
+  pylinkage.topology package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -222,13 +222,13 @@ 
    Submodules
    >>> from pylinkage.hypergraph import HypergraphLinkage, Node, Edge, NodeRole
 >>> # Four-bar linkage: 4 nodes, 3 driven edges + ground = 4 links, 4 joints
 >>> hg = HypergraphLinkage()
->>> hg.add_node(Node("A", role=NodeRole.GROUND))
->>> hg.add_node(Node("B", role=NodeRole.DRIVER))
->>> hg.add_node(Node("C", role=NodeRole.DRIVEN))
->>> hg.add_node(Node("D", role=NodeRole.GROUND))
->>> hg.add_edge(Edge("AB", "A", "B"))
->>> hg.add_edge(Edge("BC", "B", "C"))
->>> hg.add_edge(Edge("CD", "C", "D"))
+>>> hg.add_node(Node("A", role=NodeRole.GROUND))
+>>> hg.add_node(Node("B", role=NodeRole.DRIVER))
+>>> hg.add_node(Node("C", role=NodeRole.DRIVEN))
+>>> hg.add_node(Node("D", role=NodeRole.GROUND))
+>>> hg.add_edge(Edge("AB", "A", "B"))
+>>> hg.add_edge(Edge("BC", "B", "C"))
+>>> hg.add_edge(Edge("CD", "C", "D"))
 >>> compute_dof(hg)
 1
 
    
@@ -884,13 +884,13 @@ 
    Module contents
    >>> from pylinkage.hypergraph import HypergraphLinkage, Node, Edge, NodeRole
 >>> # Four-bar linkage: 4 nodes, 3 driven edges + ground = 4 links, 4 joints
 >>> hg = HypergraphLinkage()
->>> hg.add_node(Node("A", role=NodeRole.GROUND))
->>> hg.add_node(Node("B", role=NodeRole.DRIVER))
->>> hg.add_node(Node("C", role=NodeRole.DRIVEN))
->>> hg.add_node(Node("D", role=NodeRole.GROUND))
->>> hg.add_edge(Edge("AB", "A", "B"))
->>> hg.add_edge(Edge("BC", "B", "C"))
->>> hg.add_edge(Edge("CD", "C", "D"))
+>>> hg.add_node(Node("A", role=NodeRole.GROUND))
+>>> hg.add_node(Node("B", role=NodeRole.DRIVER))
+>>> hg.add_node(Node("C", role=NodeRole.DRIVEN))
+>>> hg.add_node(Node("D", role=NodeRole.GROUND))
+>>> hg.add_edge(Edge("AB", "A", "B"))
+>>> hg.add_edge(Edge("BC", "B", "C"))
+>>> hg.add_edge(Edge("CD", "C", "D"))
 >>> compute_dof(hg)
 1
 
    
diff --git a/docs/api/pylinkage.visualizer.html b/docs/api/pylinkage.visualizer.html
index d5d834f..32cd91f 100644
--- a/docs/api/pylinkage.visualizer.html
+++ b/docs/api/pylinkage.visualizer.html
@@ -6,14 +6,14 @@
   
 
   
-  pylinkage.visualizer package — pylinkage 1.2.2 documentation
+  pylinkage.visualizer package — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -370,7 +370,7 @@ 
    Submodules>>> drawing = plot_linkage_svg_with_velocity(
 ...     linkage, positions[0], velocities[0]
 ... )
->>> drawing.save_svg("linkage_with_velocity.svg")
+>>> drawing.save_svg("linkage_with_velocity.svg")
 
    
 
    
 
@@ -435,7 +435,7 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.visualizer import plot_linkage_dxf, save_linkage_dxf
 >>> doc = plot_linkage_dxf(linkage)
->>> doc.saveas("linkage.dxf")
+>>> doc.saveas("linkage.dxf")
 
    
 
    
 
@@ -456,7 +456,7 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.visualizer import save_linkage_dxf
->>> save_linkage_dxf(linkage, "output.dxf")
+>>> save_linkage_dxf(linkage, "output.dxf")
 
    
 
    
 
@@ -491,7 +491,7 @@ 
    SubmodulesExample
    
 
    >>> linkage.set_input_velocity(crank, omega=10.0)
->>> fig = animate_kinematics(linkage, show_velocity=True, save_path="vel.gif")
+>>> fig = animate_kinematics(linkage, show_velocity=True, save_path="vel.gif")
 
    
 
    
 
@@ -981,7 +981,7 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.visualizer import build_linkage_3d, save_linkage_step
 >>> model = build_linkage_3d(linkage)
->>> save_linkage_step(linkage, "linkage.step")
+>>> save_linkage_step(linkage, "linkage.step")
 
    
 
    
 
@@ -1002,7 +1002,7 @@ 
    SubmodulesExample
    
 
    >>> from pylinkage.visualizer import save_linkage_step
->>> save_linkage_step(linkage, "output.step")
+>>> save_linkage_step(linkage, "output.step")
 
    
 
    
 
diff --git a/docs/benchmarks.html b/docs/benchmarks.html
index 5e7fa66..8850276 100644
--- a/docs/benchmarks.html
+++ b/docs/benchmarks.html
@@ -6,14 +6,14 @@
   
 
   
-  Benchmarks — pylinkage 1.2.2 documentation
+  Benchmarks — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/changeloglink.html b/docs/changeloglink.html
index 8d233c2..62f7a5a 100644
--- a/docs/changeloglink.html
+++ b/docs/changeloglink.html
@@ -6,14 +6,14 @@
   
 
   
-  Changelog — pylinkage 1.2.2 documentation
+  Changelog — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -47,56 +47,62 @@
 
  • Readme
    • 
 
  • Changelog
    • 
 
    
@@ -243,14 +243,14 @@ 
    Alternative: Links-First Builder# Define links by their lengths, then connect with joints
 mechanism = (
-    MechanismBuilder("four-bar")
-    .add_ground_link("ground", ports={"O1": (0, 0), "O2": (4, 0)})
-    .add_driver_link("crank", length=1.0, motor_port="O1", omega=0.1)
-    .add_link("coupler", length=3.5)
-    .add_link("rocker", length=3.0)
-    .connect("crank.tip", "coupler.0")
-    .connect("coupler.1", "rocker.0")
-    .connect("rocker.1", "ground.O2")
+    MechanismBuilder("four-bar")
+    .add_ground_link("ground", ports={"O1": (0, 0), "O2": (4, 0)})
+    .add_driver_link("crank", length=1.0, motor_port="O1", omega=0.1)
+    .add_link("coupler", length=3.5)
+    .add_link("rocker", length=3.0)
+    .connect("crank.tip", "coupler.0")
+    .connect("coupler.1", "rocker.0")
+    .connect("rocker.1", "ground.O2")
     .build()
 )
 
@@ -287,7 +287,7 @@ 
    Symbolic Analysisimport numpy as np
 
 linkage = fourbar_symbolic(ground_length=4, crank_length=1, coupler_length=3, rocker_length=3)
-params = {"L1": 1.0, "L2": 3.0, "L3": 3.0}
+params = {"L1": 1.0, "L2": 3.0, "L3": 3.0}
 trajectories = compute_trajectory_numeric(linkage, params, np.linspace(0, 2*np.pi, 100))
 
    
 
    
@@ -455,7 +455,8 @@ 
    Stability
 
    Requirements
    
 
      
-
    • Python >= 3.10
      • 
+
    • Python >= 3.11 (tested up to 3.15; STEP export via the cad extra is not yet
+available on 3.15)
      • 
 
    • Core: numpy, tqdm
      • 
 
    • Optional (via extras): numba, scipy, sympy, matplotlib, plotly, drawsvg
      • 
 
    
diff --git a/docs/search.html b/docs/search.html
index 902ca9c..bc2e568 100644
--- a/docs/search.html
+++ b/docs/search.html
@@ -5,7 +5,7 @@
 
   
   
-  Search — pylinkage 1.2.2 documentation
+  Search — pylinkage 1.3.0 documentation
       
       
 
@@ -13,7 +13,7 @@
     
       
       
-      
+      
       
       
     
diff --git a/docs/searchindex.js b/docs/searchindex.js
index 1d36f93..137a47c 100644
--- a/docs/searchindex.js
+++ b/docs/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles":{"1. Correction":[[24,"correction"]],"2. Warning":[[24,"warning"]],"2D Pareto Front":[[37,"d-pareto-front"]],"3. Temporary Ban":[[24,"temporary-ban"]],"4. 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Numeric":[[39,"converting-back-to-numeric"]],"Converting Graph to Mechanism":[[34,"converting-graph-to-mechanism"]],"Converting to a Mechanism":[[34,"converting-to-a-mechanism"]],"Core Concepts":[[33,"core-concepts"]],"Core Features":[[35,"core-features"]],"Creating Linkages from Dimensions":[[40,"creating-linkages-from-dimensions"]],"Creating Linkages from Link Lengths":[[18,"creating-linkages-from-link-lengths"]],"Creating Symbolic Linkages":[[39,"creating-symbolic-linkages"]],"Creating a Hypergraph Linkage":[[34,"creating-a-hypergraph-linkage"]],"Currently deprecated":[[25,"currently-deprecated"]],"Custom Components":[[32,null]],"Customizing DXF Output":[[41,"customizing-dxf-output"]],"Customizing Plotly Appearance":[[41,"customizing-plotly-appearance"]],"Customizing STEP Dimensions":[[41,"customizing-step-dimensions"]],"Customizing SVG Style":[[41,"customizing-svg-style"]],"DXF Export (2D CAD)":[[41,"dxf-export-2d-cad"]],"Decomposing a Linkage":[[34,"decomposing-a-linkage"]],"Define and Visualize a Four-Bar Linkage":[[29,"define-and-visualize-a-four-bar-linkage"]],"Defining a Fitness Function":[[30,"defining-a-fitness-function"]],"Deprecated":[[23,"deprecated"],[23,"id22"]],"Deprecated in 0.5.3":[[23,"deprecated-in-0-5-3"]],"Deprecated in 0.6.0":[[23,"deprecated-in-0-6-0"]],"Deprecated in 0.7.0":[[23,"deprecated-in-0-7-0"]],"Deprecations":[[25,null]],"Embedding in Web Pages":[[41,"embedding-in-web-pages"]],"Enforcement":[[24,"enforcement"]],"Enforcement Guidelines":[[24,"enforcement-guidelines"]],"Enforcement Responsibilities":[[24,"enforcement-responsibilities"]],"Environment":[[22,"environment"]],"Example Complete Workflow":[[38,"example-complete-workflow"]],"Example Objective Functions":[[39,"example-objective-functions"]],"Example Scripts":[[26,null]],"Example: Cam-Driven Four-Bar":[[31,"example-cam-driven-four-bar"]],"Example: Complete Visualization Workflow":[[41,"example-complete-visualization-workflow"]],"Example: Minimize Peak Velocity":[[36,"example-minimize-peak-velocity"]],"Example: Optimizing for Path Shape":[[30,"example-optimizing-for-path-shape"]],"Example: Oscillating Joint":[[32,"example-oscillating-joint"]],"Example: Slider Joint":[[32,"example-slider-joint"]],"Example: Three Precision Points":[[40,"example-three-precision-points"]],"Example: Uniform Velocity Profile":[[36,"example-uniform-velocity-profile"]],"Example: Velocity Direction Constraint":[[36,"example-velocity-direction-constraint"]],"Exporting Multiple Frames":[[41,"exporting-multiple-frames"]],"Exporting to DataFrame":[[38,"exporting-to-dataframe"]],"Fast Pre-Compiled Functions":[[39,"fast-pre-compiled-functions"]],"Filtering Solutions":[[37,"filtering-solutions"]],"Fixed":[[23,"fixed"],[23,"id3"],[23,"id6"],[23,"id10"],[23,"id12"],[23,"id18"],[23,"id21"],[23,"id27"]],"Fixed in 0.2.1":[[23,"fixed-in-0-2-1"]],"Fixed in 0.2.2":[[23,"fixed-in-0-2-2"]],"Fixed in 0.3.0":[[23,"fixed-in-0-3-0"]],"Fixed in 0.4.0":[[23,"fixed-in-0-4-0"]],"Fixed in 0.5.0":[[23,"fixed-in-0-5-0"]],"Fixed in 0.5.3":[[23,"fixed-in-0-5-3"]],"Fixed in 0.6.0":[[23,"fixed-in-0-6-0"]],"Fixed in 0.7.0":[[23,"fixed-in-0-7-0"]],"Four-Pose and Five-Pose Synthesis":[[40,"four-pose-and-five-pose-synthesis"]],"Four-bar Linkage":[[26,"four-bar-linkage"]],"Function Generation":[[40,"function-generation"]],"FunctionProfile":[[31,"functionprofile"]],"Generating Bounds":[[30,"generating-bounds"]],"Getting Started":[[33,null],[35,"getting-started"]],"Graph-Based Linkage Representation":[[34,null]],"Grashof Analysis":[[40,"grashof-analysis"]],"Grid Search Optimization":[[30,"grid-search-optimization"]],"Handling Errors":[[33,"handling-errors"]],"How deprecation works here":[[25,"how-deprecation-works-here"]],"Hypergraph Representation":[[34,"hypergraph-representation"]],"Hypervolume Indicator":[[37,"hypervolume-indicator"]],"Illustrated Example: Effect of Link Lengths":[[39,"illustrated-example-effect-of-link-lengths"]],"Including Transmission Angle":[[38,"including-transmission-angle"]],"Indices and tables":[[28,"indices-and-tables"]],"Installation":[[29,"installation"],[33,"installation"],[37,"installation"]],"Introduction":[[28,null],[31,"introduction"]],"Inverted Stroke Engine":[[26,"inverted-stroke-engine"]],"Isomorphism Detection":[[34,"isomorphism-detection"]],"Kinematics-Based Optimization":[[36,null]],"Linkage Synthesis":[[40,null]],"Matplotlib Backend":[[41,"matplotlib-backend"]],"Matplotlib Visualization":[[36,"matplotlib-visualization"]],"Method 1: fourbar_symbolic (Recommended)":[[39,"method-1-fourbar-symbolic-recommended"]],"Method 2: Building from SymJoint Classes":[[39,"method-2-building-from-symjoint-classes"]],"Migrating":[[25,"migrating"]],"Mobility Analysis":[[34,"mobility-analysis"]],"Module 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\ No newline at end of file
diff --git a/docs/tutorials/advanced_optimization.html b/docs/tutorials/advanced_optimization.html
index 94d2699..fd897f2 100644
--- a/docs/tutorials/advanced_optimization.html
+++ b/docs/tutorials/advanced_optimization.html
@@ -6,14 +6,14 @@
   
 
   
-  Advanced Optimization Techniques — pylinkage 1.2.2 documentation
+  Advanced Optimization Techniques — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -144,7 +144,7 @@ 
    Basic Fitness Function@pl.kinematic_minimization
 def fitness(loci, **kwargs):
-    """Evaluate linkage fitness.
+    """Evaluate linkage fitness.
 
     :param loci: Joint positions for each simulation step.
         Structure: tuple[tuple[tuple[float, float], ...], ...]
@@ -154,7 +154,7 @@ 
    Basic Fitness Function    :param kwargs: ``linkage``, ``params`` (the candidate constraints)
         and ``init_pos`` (the joint positions the simulation started from).
     :return: Fitness score (lower is better for minimization)
-    """
+    """
     # Get the locus (path) of the last joint
     output_locus = [step[-1] for step in loci]
 
@@ -181,7 +181,7 @@ 
    Working with Loci DataUnderstanding the loci structure is key to writing good fitness functions:
    
 
    @pl.kinematic_minimization
 def analyze_loci(loci, **kwargs):
-    """Example showing loci structure."""
+    """Example showing loci structure."""
     # loci[step][joint] = (x, y)
 
     # Get all positions of joint 0 (usually the crank)
@@ -197,7 +197,7 @@ 
    Working with Loci Databbox = pl.bounding_box(output_path)
     # bbox = (min_y, max_x, max_y, min_x)
 
-    # Score: the crank's highest point should stay under the output's
+    # Score: the crank's highest point should stay under the output's
     return max(y for _, y in crank_path) - bbox[2]
 
    
 
    
@@ -214,22 +214,22 @@ 
    Example: Optimizing for Path Shapedef create_linkage():
-    """Create the base linkage to optimize."""
-    A = Ground(0.0, 0.0, name="A")
-    D = Ground(3.0, 0.0, name="D")
+    """Create the base linkage to optimize."""
+    A = Ground(0.0, 0.0, name="A")
+    D = Ground(3.0, 0.0, name="D")
     crank = Crank(
-        anchor=A, radius=1.0, angular_velocity=0.31, name="Crank",
+        anchor=A, radius=1.0, angular_velocity=0.31, name="Crank",
     )
     output = RRRDyad(
         anchor1=crank.output, anchor2=D,
-        distance1=3.0, distance2=1.0, name="Output",
+        distance1=3.0, distance2=1.0, name="Output",
     )
     return Linkage([A, D, crank, output])
 
 
 @pl.kinematic_minimization
 def rectangle_fitness(loci, **kwargs):
-    """Minimize distance from a target rectangle."""
+    """Minimize distance from a target rectangle."""
     output_path = [step[-1] for step in loci]
     bbox = pl.bounding_box(output_path)
 
@@ -259,8 +259,8 @@ 
    Example: Optimizing for Path Shape# Every optimizer returns an Ensemble: the optimized linkage plus one
 # Member per candidate kept, best first.
 best = results[0]
-print(f"Best score: {best.score}")
-print(f"Best constraints: {best.dimensions}")
+print(f"Best score: {best.score}")
+print(f"Best constraints: {best.dimensions}")
 
 # Animate the best member: the Ensemble simulates it from the joint
 # positions the search started from, then hands the loci to show_linkage
@@ -297,8 +297,8 @@ 
    Particle Swarm Optimization Parametersdimensions=None,
 
     # Swarm dynamics
-    leader=3.0,           # Pull towards the neighbourhood's best
-    follower=0.1,         # Pull towards the particle's own best
+    leader=3.0,           # Pull towards the neighbourhood's best
+    follower=0.1,         # Pull towards the particle's own best
     inertia=0.6,          # Momentum
     neighbors=17,         # Ring-topology neighbourhood size
 
@@ -346,7 +346,7 @@ 
    Grid Search Optimizationorder_relation=min,    # min or max
     verbose=False,
 )
-print(f"{len(results)} candidates kept, best score {results[0].score:.3f}")
+print(f"{len(results)} candidates kept, best score {results[0].score:.3f}")
 
 # Note: Grid search is O(divisions^n) where n = number of constraints
 # Use sparingly for high-dimensional problems
@@ -359,7 +359,7 @@ 
    Multi-Objective Optimization
    @pl.kinematic_minimization
 def weighted_objectives(loci, **kwargs):
-    """Combine objectives with weights (simple approach)."""
+    """Combine objectives with weights (simple approach)."""
     output_path = [step[-1] for step in loci]
 
     # Objective 1: Match target bounding box
@@ -384,11 +384,11 @@ 
    Constraint PreservationSometimes you want to optimize only certain constraints while keeping others fixed:
    
 
    @pl.kinematic_minimization
 def constrained_fitness(loci, params, **kwargs):
-    """Fitness function that enforces additional constraints."""
+    """Fitness function that enforces additional constraints."""
     # Penalize if the crank radius (first constraint of this
     # linkage) is too short
     if params[0] < 0.5:
-        return float('inf')
+        return float('inf')
 
     # Normal fitness calculation
     output_path = [step[-1] for step in loci]
@@ -427,7 +427,7 @@ 
    Visualizing Optimization Progressdef tracking_fitness(linkage, constraints, initial_positions):
-    """Wrapper that records every evaluation."""
+    """Wrapper that records every evaluation."""
     score = rectangle_fitness(linkage, constraints, initial_positions)
     history.append((score, list(constraints), initial_positions))
     return score
@@ -447,11 +447,11 @@ 
    Visualizing Optimization Progress# Analyze history: one entry per particle per iteration, after the
 # initial swarm
 scores = [h[0] for h in history]
-print(f"Evaluations: {len(scores)}, best score: {min(scores):.3f}")
+print(f"Evaluations: {len(scores)}, best score: {min(scores):.3f}")
 first_iteration = scores[:20]
 last_iteration = scores[-20:]
-print(f"Best of first iteration: {min(first_iteration):.3f}")
-print(f"Best of last iteration:  {min(last_iteration):.3f}")
+print(f"Best of first iteration: {min(first_iteration):.3f}")
+print(f"Best of last iteration:  {min(last_iteration):.3f}")
 
    
 
    
 
    The pylinkage.visualizer PSO plots (parallel_coordinates_plot,
@@ -470,9 +470,9 @@ 
    Async Optimizationdef on_progress(progress):
         if progress.current_iteration % 10 == 0:
             print(
-                f"Iteration {progress.current_iteration}"
-                f"/{progress.total_iterations}: "
-                f"best = {progress.best_score}"
+                f"Iteration {progress.current_iteration}"
+                f"/{progress.total_iterations}: "
+                f"best = {progress.best_score}"
             )
 
     results = await particle_swarm_optimization_async(
@@ -489,7 +489,7 @@ 
    Async Optimization# Run async optimization
 results = asyncio.run(optimize_with_progress())
-print(f"Async result: {results[0].score:.3f}")
+print(f"Async result: {results[0].score:.3f}")
 
    
 
    
 
    The optimization runs in a thread-pool executor, so the event loop stays
diff --git a/docs/tutorials/cam_follower.html b/docs/tutorials/cam_follower.html
index bbd7daa..7e1c9ab 100644
--- a/docs/tutorials/cam_follower.html
+++ b/docs/tutorials/cam_follower.html
@@ -6,14 +6,14 @@
   
 
   
-  Cam-Follower Mechanisms — pylinkage 1.2.2 documentation
+  Cam-Follower Mechanisms — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -241,14 +241,14 @@ 
    Basic Examplefrom pylinkage.cam import FunctionProfile, HarmonicMotionLaw
 
 # Fixed cam center
-cam_center = Ground(0.0, 0.0, name="cam_center")
+cam_center = Ground(0.0, 0.0, name="cam_center")
 
 # Cam driver (rotating crank)
 cam_crank = Crank(
     anchor=cam_center,
     radius=0.1,           # Small radius (just for visualization)
     angular_velocity=0.1, # Rotation speed
-    name="cam"
+    name="cam"
 )
 
 # Cam profile
@@ -263,7 +263,7 @@ 
    Basic Example)
 
 # Guide point (defines direction of follower motion)
-guide = Ground(0.0, 1.5, name="guide")
+guide = Ground(0.0, 1.5, name="guide")
 
 # Translating follower
 follower = TranslatingCamFollower(
@@ -272,19 +272,19 @@ 
    Basic Exampleguide=guide,
     guide_angle=math.pi/2,  # Vertical motion
     roller_radius=0.0,      # Knife-edge follower
-    name="follower"
+    name="follower"
 )
 
 # Create linkage
 linkage = Linkage(
     components=[cam_center, guide, cam_crank, follower],
-    name="Cam mechanism"
+    name="Cam mechanism"
 )
 
 # Simulate
 for positions in linkage.step():
     follower_pos = follower.output.position
-    print(f"Follower at: {follower_pos}")
+    print(f"Follower at: {follower_pos}")
 
    
 
    
 
@@ -315,8 +315,8 @@ 
    Basic Example
 from pylinkage.cam import FunctionProfile, CycloidalMotionLaw
 
 # Fixed points
-cam_center = Ground(0.0, 0.0, name="cam_center")
-pivot = Ground(2.0, 0.0, name="pivot")
+cam_center = Ground(0.0, 0.0, name="cam_center")
+pivot = Ground(2.0, 0.0, name="pivot")
 
 # Cam driver
 cam_crank = Crank(
@@ -352,7 +352,7 @@ 
    Basic Example
 
 for positions in linkage.step():
     output_pos = follower.output.position
-    print(f"Arm end at: {output_pos}")
+    print(f"Arm end at: {output_pos}")
 
    
 
    
 
@@ -371,9 +371,9 @@ 
    Example: Cam-Driven Four-Barfrom pylinkage.cam import FunctionProfile, HarmonicMotionLaw
 
 # Ground points
-cam_center = Ground(0.0, 0.0, name="cam_center")
-guide = Ground(0.0, 2.0, name="guide")
-rocker_pivot = Ground(3.0, 0.0, name="rocker_pivot")
+cam_center = Ground(0.0, 0.0, name="cam_center")
+guide = Ground(0.0, 2.0, name="guide")
+rocker_pivot = Ground(3.0, 0.0, name="rocker_pivot")
 
 # Cam mechanism
 cam_crank = Crank(anchor=cam_center, radius=0.1, angular_velocity=0.1)
@@ -414,7 +414,7 @@ 
    Example: Cam-Driven Four-Bar# solves, so its position is read directly; only actuators and cam
 # followers expose a separate ``output``.
 for positions in linkage.step():
-    print(f"Rocker joint at: {rocker.position}")
+    print(f"Rocker joint at: {rocker.position}")
 
    
 
    
 
@@ -431,7 +431,7 @@ 
    Pressure Angle# Check pressure angle at various cam positions
 for angle in [0, math.pi/4, math.pi/2, math.pi]:
     pressure = profile.pressure_angle(angle)
-    print(f"At {math.degrees(angle):.0f} deg: pressure angle = {math.degrees(pressure):.1f} deg")
+    print(f"At {math.degrees(angle):.0f} deg: pressure angle = {math.degrees(pressure):.1f} deg")
 
    
 
    
 
@@ -441,7 +441,7 @@ 
    Pitch Radius
    roller_radius = 0.1
 for angle in [0, math.pi/4, math.pi/2]:
     pitch = profile.pitch_radius(angle, roller_radius)
-    print(f"Pitch radius at {math.degrees(angle):.0f} deg: {pitch:.3f}")
+    print(f"Pitch radius at {math.degrees(angle):.0f} deg: {pitch:.3f}")
 
    
 
    
 
diff --git a/docs/tutorials/custom_joints.html b/docs/tutorials/custom_joints.html
index a5713fc..7f09eab 100644
--- a/docs/tutorials/custom_joints.html
+++ b/docs/tutorials/custom_joints.html
@@ -6,14 +6,14 @@
   
 
   
-  Custom Components — pylinkage 1.2.2 documentation
+  Custom Components — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -155,23 +155,23 @@ 
    Step 1: Define the Classclass Slider(BinaryDyad):
-    """A joint that sits a fraction ``t`` of the way from anchor1 to anchor2.
+    """A joint that sits a fraction ``t`` of the way from anchor1 to anchor2.
 
     - t=0 puts the joint on anchor1
     - t=1 puts the joint on anchor2
     - values in between interpolate linearly
-    """
+    """
 
-    __slots__ = ("t",)
+    __slots__ = ("t",)
 
     def __init__(self, anchor1, anchor2, t=0.5, name=None):
-        """Create a Slider joint.
+        """Create a Slider joint.
 
         :param anchor1: Parent component at the start of the slide.
         :param anchor2: Parent component at the end of the slide.
         :param t: Position parameter (0 to 1).
         :param name: Joint name.
-        """
+        """
         super().__init__(None, None, name)  # position is computed below
         self.anchor1 = anchor1
         self.anchor2 = anchor2
@@ -184,7 +184,7 @@ 
    Step 1: Define the Class
    
 
    Return the geometric parameters that define this joint’s motion:
    
 
    def get_constraints(self):
-    """Return the slide parameter as constraint."""
+    """Return the slide parameter as constraint."""
     return (self.t,)
 
    
 
    
@@ -195,10 +195,10 @@ 
    Step 3: Implement set_constraintsget_constraints returned; the trailing
 *args keeps the signature compatible with the built-in dyads:
    
 
    def set_constraints(self, t=None, *args):
-    """Set the slide parameter.
+    """Set the slide parameter.
 
     :param t: New position parameter (0 to 1).
-    """
+    """
     if t is not None:
         self.t = t
 
    
@@ -210,14 +210,14 @@ 
    Step 4: Implement reload_get_anchor_position reads either a component or an
 actuator’s output proxy:
    
 
    def reload(self, dt=1):
-    """Recompute position by interpolating between the anchors.
+    """Recompute position by interpolating between the anchors.
 
     :param dt: Time step (unused: the slider does not move on its own).
-    """
+    """
     x0, y0 = self._get_anchor_position(self.anchor1)
     x1, y1 = self._get_anchor_position(self.anchor2)
     if None in (x0, y0, x1, y1):
-        raise ValueError(f"{self.name}: anchors have no position yet")
+        raise ValueError(f"{self.name}: anchors have no position yet")
 
     # Linear interpolation
     self.x = x0 + self.t * (x1 - x0)
@@ -233,9 +233,9 @@ 
    Complete Slider Implementationclass Slider(BinaryDyad):
-    """A joint that sits a fraction ``t`` of the way from anchor1 to anchor2."""
+    """A joint that sits a fraction ``t`` of the way from anchor1 to anchor2."""
 
-    __slots__ = ("t",)
+    __slots__ = ("t",)
 
     def __init__(self, anchor1, anchor2, t=0.5, name=None):
         super().__init__(None, None, name)
@@ -255,7 +255,7 @@ 
    Complete Slider Implementationx0, y0 = self._get_anchor_position(self.anchor1)
         x1, y1 = self._get_anchor_position(self.anchor2)
         if None in (x0, y0, x1, y1):
-            raise ValueError(f"{self.name}: anchors have no position yet")
+            raise ValueError(f"{self.name}: anchors have no position yet")
         self.x = x0 + self.t * (x1 - x0)
         self.y = y0 + self.t * (y1 - y0)
 
    
@@ -273,28 +273,28 @@ 
    Using the Custom Componentfrom pylinkage.simulation import Linkage
 
 # The rail
-p1 = Ground(0.0, 0.0, name="P1")
-p2 = Ground(4.0, 0.0, name="P2")
+p1 = Ground(0.0, 0.0, name="P1")
+p2 = Ground(4.0, 0.0, name="P2")
 
 # A pivot halfway along it (custom component, see above)
-pivot = Slider(anchor1=p1, anchor2=p2, t=0.5, name="Pivot")
+pivot = Slider(anchor1=p1, anchor2=p2, t=0.5, name="Pivot")
 
 # A crank, and a rocker between the crank tip and the pivot
-motor = Ground(1.0, 3.0, name="Motor")
-crank = Crank(anchor=motor, radius=1.0, angular_velocity=0.1, name="Crank")
+motor = Ground(1.0, 3.0, name="Motor")
+crank = Crank(anchor=motor, radius=1.0, angular_velocity=0.1, name="Crank")
 rocker = RRRDyad(
     anchor1=crank.output,
     anchor2=pivot,
     distance1=3.0,
     distance2=2.5,
-    name="Rocker",
+    name="Rocker",
 )
 
-linkage = Linkage([p1, p2, motor, pivot, crank, rocker], name="Sliding pivot")
+linkage = Linkage([p1, p2, motor, pivot, crank, rocker], name="Sliding pivot")
 
 loci = list(linkage.step())
-print(f"Pivot at {pivot.position}, {len(loci)} steps simulated")
-print(f"Constraints: {linkage.get_constraints()}")
+print(f"Pivot at {pivot.position}, {len(loci)} steps simulated")
+print(f"Constraints: {linkage.get_constraints()}")
 
 pl.show_linkage(linkage)
 
    
@@ -310,7 +310,7 @@ 
    Using the Custom Component
    @pl.kinematic_maximization
 def stride(loci, **kwargs):
-    """Horizontal travel of the rocker joint."""
+    """Horizontal travel of the rocker joint."""
     xs = [step[-1][0] for step in loci]
     return max(xs) - min(xs)
 
@@ -325,7 +325,7 @@ 
    Using the Custom Componentn_particles=20, iterations=20, verbose=False,
 )
 best = results[0]
-print(f"Stride {best.score:.3f} with the pivot at t={best.dimensions[0]:.2f}")
+print(f"Stride {best.score:.3f} with the pivot at t={best.dimensions[0]:.2f}")
 
    
 
    
 
@@ -340,18 +340,18 @@ 
    Example: Oscillating Jointclass Oscillator(ConnectedComponent):
-    """A joint that moves sinusoidally around a center point."""
+    """A joint that moves sinusoidally around a center point."""
 
-    __slots__ = ("anchor", "amplitude", "period", "_time")
+    __slots__ = ("anchor", "amplitude", "period", "_time")
 
     def __init__(self, anchor, amplitude=1.0, period=60, name=None):
-        """Create an oscillating joint.
+        """Create an oscillating joint.
 
         :param anchor: Center point of oscillation.
         :param amplitude: Maximum displacement from center.
         :param period: Steps per oscillation.
         :param name: Joint name.
-        """
+        """
         super().__init__(None, None, name)
         self.anchor = anchor
         self.amplitude = amplitude
@@ -378,12 +378,12 @@ 
    Example: Oscillating Jointself._time += dt
 
 
-centre = Ground(0.0, 2.0, name="Centre")
-oscillator = Oscillator(centre, amplitude=1.0, period=60, name="Oscillator")
+centre = Ground(0.0, 2.0, name="Centre")
+oscillator = Oscillator(centre, amplitude=1.0, period=60, name="Oscillator")
 linkage = Linkage([centre, oscillator])
 
 xs = [step[-1][0] for step in linkage.step(iterations=60)]
-print(f"x swings between {min(xs):.2f} and {max(xs):.2f}")
+print(f"x swings between {min(xs):.2f} and {max(xs):.2f}")
 
    
 
    
 
    Expected output:
    
diff --git a/docs/tutorials/getting_started.html b/docs/tutorials/getting_started.html
index 7a65d53..0c48e52 100644
--- a/docs/tutorials/getting_started.html
+++ b/docs/tutorials/getting_started.html
@@ -6,14 +6,14 @@
   
 
   
-  Getting Started — pylinkage 1.2.2 documentation
+  Getting Started — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -180,15 +180,15 @@ 
    Step 2: Define the componentsfrom pylinkage.simulation import Linkage
 
 # Ground anchors — two fixed points on the frame.
-A = Ground(0.0, 0.0, name="A")
-D = Ground(3.0, 0.0, name="D")
+A = Ground(0.0, 0.0, name="A")
+D = Ground(3.0, 0.0, name="D")
 
 # Crank — rotates about A with radius 1, one step = 0.31 rad.
 crank = Crank(
     anchor=A,
     radius=1.0,
     angular_velocity=0.31,
-    name="Crank",
+    name="Crank",
 )
 
 # Coupler-rocker pin joint — closes the loop between the crank tip
@@ -198,7 +198,7 @@ 
    Step 2: Define the componentsanchor2=D,
     distance1=3.0,          # coupler length (B → C)
     distance2=1.0,          # rocker length  (C → D)
-    name="Output",
+    name="Output",
 )
 
    
 
    
@@ -208,7 +208,7 @@ 
    Step 3: Create the linkageLinkage:
    
 
    linkage = Linkage(
     [A, D, crank, pin],
-    name="Four-bar linkage",
+    name="Four-bar linkage",
 )
 
    
 
    
@@ -220,9 +220,9 @@ 
    Step 4: Simulate the motionloci = tuple(linkage.step())
 
 # loci[i] is a tuple of (x, y) coordinates in the component order.
-print(f"Simulation steps: {len(loci)}")
-print(f"Final crank tip: {loci[-1][2]}")
-print(f"Final output point: {loci[-1][3]}")
+print(f"Simulation steps: {len(loci)}")
+print(f"Final crank tip: {loci[-1][2]}")
+print(f"Final output point: {loci[-1][3]}")
 
    
 
    
 
    For a numba-accelerated simulation that returns a contiguous numpy array,
@@ -269,19 +269,19 @@ 
    Complete Examplefrom pylinkage.simulation import Linkage
 
 # Components
-A = Ground(0.0, 0.0, name="A")
-D = Ground(3.0, 0.0, name="D")
-crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank")
+A = Ground(0.0, 0.0, name="A")
+D = Ground(3.0, 0.0, name="D")
+crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank")
 pin = RRRDyad(
     anchor1=crank.output,
     anchor2=D,
     distance1=3.0,
     distance2=1.0,
-    name="Output",
+    name="Output",
 )
 
 # Linkage
-linkage = Linkage([A, D, crank, pin], name="Four-bar linkage")
+linkage = Linkage([A, D, crank, pin], name="Four-bar linkage")
 
 # Visualize
 pl.show_linkage(linkage)
@@ -296,7 +296,7 @@ 
    Understanding the Constraint System
    # Get all constraints as a flat list.
 constraints = linkage.get_constraints()
-print(f"Constraints: {constraints}")
+print(f"Constraints: {constraints}")
 # → [1.0, 3.0, 1.0]  (crank radius, d1, d2 on the RRR dyad)
 
 # Modify and apply.
@@ -305,7 +305,7 @@ 
    Understanding the Constraint System# Joint positions
 coords = linkage.get_coords()
-print(f"Component positions: {coords}")
+print(f"Component positions: {coords}")
 
    
 
    
 
@@ -317,7 +317,7 @@ 
    Handling Errors
    try:
     tuple(linkage.step())
 except pl.UnbuildableError:
-    print("Linkage cannot be built with these constraints")
+    print("Linkage cannot be built with these constraints")
 
    
 
    
 
diff --git a/docs/tutorials/graph_representation.html b/docs/tutorials/graph_representation.html
index ac503b8..38f1af7 100644
--- a/docs/tutorials/graph_representation.html
+++ b/docs/tutorials/graph_representation.html
@@ -6,14 +6,14 @@
   
 
   
-  Graph-Based Linkage Representation — pylinkage 1.2.2 documentation
+  Graph-Based Linkage Representation — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
       
@@ -159,29 +159,29 @@ 
    Creating a Hypergraph Linkage# A four-bar: two grounded joints, one motor-driven crank pin, one
 # passive coupler-rocker pin
-hg = HypergraphLinkage(name="FourBar")
-hg.add_node(Node("A", role=NodeRole.GROUND))
-hg.add_node(Node("B", role=NodeRole.DRIVER))
-hg.add_node(Node("C", role=NodeRole.DRIVEN))
-hg.add_node(Node("D", role=NodeRole.GROUND))
+hg = HypergraphLinkage(name="FourBar")
+hg.add_node(Node("A", role=NodeRole.GROUND))
+hg.add_node(Node("B", role=NodeRole.DRIVER))
+hg.add_node(Node("C", role=NodeRole.DRIVEN))
+hg.add_node(Node("D", role=NodeRole.GROUND))
 
 # Three binary links: crank A-B, coupler B-C, rocker C-D. The ground
 # link between A and D is implied by their role.
-hg.add_edge(Edge("AB", "A", "B"))
-hg.add_edge(Edge("BC", "B", "C"))
-hg.add_edge(Edge("CD", "C", "D"))
-
-print(f"Nodes: {list(hg.nodes)}")
-print(f"Edges: {[(e.id, e.source, e.target) for e in hg.edges.values()]}")
-print(f"Grounds: {[n.id for n in hg.ground_nodes()]}")
-print(f"Drivers: {[n.id for n in hg.driver_nodes()]}")
+hg.add_edge(Edge("AB", "A", "B"))
+hg.add_edge(Edge("BC", "B", "C"))
+hg.add_edge(Edge("CD", "C", "D"))
+
+print(f"Nodes: {list(hg.nodes)}")
+print(f"Edges: {[(e.id, e.source, e.target) for e in hg.edges.values()]}")
+print(f"Grounds: {[n.id for n in hg.ground_nodes()]}")
+print(f"Drivers: {[n.id for n in hg.driver_nodes()]}")
 
    
 
    
 
    Expected output:
    
-
    Nodes: ['A', 'B', 'C', 'D']
-Edges: [('AB', 'A', 'B'), ('BC', 'B', 'C'), ('CD', 'C', 'D')]
-Grounds: ['A', 'D']
-Drivers: ['B']
+
    Nodes: ['A', 'B', 'C', 'D']
+Edges: [('AB', 'A', 'B'), ('BC', 'B', 'C'), ('CD', 'C', 'D')]
+Grounds: ['A', 'D']
+Drivers: ['B']
 
    
 
    
 
@@ -205,9 +205,9 @@ 
    Attaching Dimensionscx, cy = (bx + dx) / 2, math.sqrt(COUPLER**2 - half**2)
 
 dims = Dimensions(
-    node_positions={"A": (0, 0), "B": (bx, by), "C": (cx, cy), "D": (dx, dy)},
-    driver_angles={"B": DriverAngle(angular_velocity=OMEGA)},
-    edge_distances={"AB": CRANK, "BC": COUPLER, "CD": ROCKER},
+    node_positions={"A": (0, 0), "B": (bx, by), "C": (cx, cy), "D": (dx, dy)},
+    driver_angles={"B": DriverAngle(angular_velocity=OMEGA)},
+    edge_distances={"AB": CRANK, "BC": COUPLER, "CD": ROCKER},
 )
 
 # Consistency check without raising: an empty list means valid
@@ -222,8 +222,8 @@ 
    Converting to a Mechanismmechanism = to_mechanism(hg, dims)
 loci = list(mechanism.step())
 
-print(f"Mechanism joints: {[j.id for j in mechanism.joints]}")
-print(f"Simulation steps: {len(loci)}")
+print(f"Mechanism joints: {[j.id for j in mechanism.joints]}")
+print(f"Simulation steps: {len(loci)}")
 
 # The Mechanism draws and animates like a Linkage
 import pylinkage as pl
@@ -231,7 +231,7 @@ 
    Converting to a Mechanism
    Mechanism joints: ['A', 'D', 'B', 'C']
+
    Mechanism joints: ['A', 'D', 'B', 'C']
 Simulation steps: 60
 
    
 
    
@@ -246,39 +246,39 @@ 
    Ternary Links via HyperedgeDimensions fully describes the triangle.
    
 
    from pylinkage.hypergraph import Hyperedge
 
-hg_coupler = HypergraphLinkage(name="CouplerFourBar")
+hg_coupler = HypergraphLinkage(name="CouplerFourBar")
 for node_id, role in [
-    ("A", NodeRole.GROUND), ("B", NodeRole.DRIVER), ("C", NodeRole.DRIVEN),
-    ("P", NodeRole.DRIVEN), ("D", NodeRole.GROUND),
+    ("A", NodeRole.GROUND), ("B", NodeRole.DRIVER), ("C", NodeRole.DRIVEN),
+    ("P", NodeRole.DRIVEN), ("D", NodeRole.GROUND),
 ]:
     hg_coupler.add_node(Node(node_id, role=role))
 
-hg_coupler.add_edge(Edge("AB", "A", "B"))
-hg_coupler.add_edge(Edge("CD", "C", "D"))
+hg_coupler.add_edge(Edge("AB", "A", "B"))
+hg_coupler.add_edge(Edge("CD", "C", "D"))
 # All three sides of the coupler triangle: this is what makes it rigid
-hg_coupler.add_edge(Edge("BC", "B", "C"))
-hg_coupler.add_edge(Edge("BP", "B", "P"))
-hg_coupler.add_edge(Edge("CP", "C", "P"))
+hg_coupler.add_edge(Edge("BC", "B", "C"))
+hg_coupler.add_edge(Edge("BP", "B", "P"))
+hg_coupler.add_edge(Edge("CP", "C", "P"))
 # The hyperedge labels the triangle as one body for topology analysis
-hg_coupler.add_hyperedge(Hyperedge("coupler", ("B", "C", "P"), name="coupler triangle"))
+hg_coupler.add_hyperedge(Hyperedge("coupler", ("B", "C", "P"), name="coupler triangle"))
 
 # P sits one unit above the middle of B-C
 ux, uy = (cx - bx) / COUPLER, (cy - by) / COUPLER
 px, py = bx + 0.5 * (cx - bx) - uy, by + 0.5 * (cy - by) + ux
 
 dims_coupler = Dimensions(
-    node_positions={"A": (0, 0), "B": (bx, by), "C": (cx, cy), "P": (px, py), "D": (dx, dy)},
-    driver_angles={"B": DriverAngle(angular_velocity=OMEGA)},
+    node_positions={"A": (0, 0), "B": (bx, by), "C": (cx, cy), "P": (px, py), "D": (dx, dy)},
+    driver_angles={"B": DriverAngle(angular_velocity=OMEGA)},
     edge_distances={
-        "AB": CRANK, "CD": ROCKER, "BC": COUPLER,
-        "BP": math.hypot(px - bx, py - by),
-        "CP": math.hypot(px - cx, py - cy),
+        "AB": CRANK, "CD": ROCKER, "BC": COUPLER,
+        "BP": math.hypot(px - bx, py - by),
+        "CP": math.hypot(px - cx, py - cy),
     },
 )
 
 coupler_mechanism = to_mechanism(hg_coupler, dims_coupler)
 coupler_path = [step[-1] for step in coupler_mechanism.step()]
-print(f"P traces {len(coupler_path)} points")
+print(f"P traces {len(coupler_path)} points")
 
    
 
    
 
@@ -291,29 +291,29 @@ 
    Building Hierarchical Linkages
    from pylinkage.hypergraph import ComponentInstance, Connection, HierarchicalLinkage
 
 # A reusable leg: motor M, knee K, foot F, hip H
-leg = HypergraphLinkage(name="leg")
-leg.add_node(Node("M", role=NodeRole.GROUND))
-leg.add_node(Node("K", role=NodeRole.DRIVER))
-leg.add_node(Node("F", role=NodeRole.DRIVEN))
-leg.add_node(Node("H", role=NodeRole.GROUND))
-leg.add_edge(Edge("MK", "M", "K"))
-leg.add_edge(Edge("KF", "K", "F"))
-leg.add_edge(Edge("FH", "F", "H"))
+leg = HypergraphLinkage(name="leg")
+leg.add_node(Node("M", role=NodeRole.GROUND))
+leg.add_node(Node("K", role=NodeRole.DRIVER))
+leg.add_node(Node("F", role=NodeRole.DRIVEN))
+leg.add_node(Node("H", role=NodeRole.GROUND))
+leg.add_edge(Edge("MK", "M", "K"))
+leg.add_edge(Edge("KF", "K", "F"))
+leg.add_edge(Edge("FH", "F", "H"))
 
 # Two legs sharing their hip pivot
-left = ComponentInstance(id="left", topology=leg, ports={"hip": "H"})
-right = ComponentInstance(id="right", topology=leg, ports={"hip": "H"})
+left = ComponentInstance(id="left", topology=leg, ports={"hip": "H"})
+right = ComponentInstance(id="right", topology=leg, ports={"hip": "H"})
 
 chassis = HierarchicalLinkage(
-    instances={"left": left, "right": right},
-    connections=[Connection("left", "hip", "right", "hip")],
-    name="two-leg chassis",
+    instances={"left": left, "right": right},
+    connections=[Connection("left", "hip", "right", "hip")],
+    name="two-leg chassis",
 )
 
 flat = chassis.flatten()
-print(f"Flattened: {len(flat.nodes)} nodes, {len(flat.edges)} edges")
+print(f"Flattened: {len(flat.nodes)} nodes, {len(flat.edges)} edges")
 for edge in flat.edges.values():
-    print(f"  {edge.id}: {edge.source} -> {edge.target}")
+    print(f"  {edge.id}: {edge.source} -> {edge.target}")
 
    
 
    
 
    Expected output:
    
@@ -363,20 +363,20 @@ 
    Decomposing a Linkagegraph = from_hypergraph(hg)
 result = decompose_assur_groups(graph)
 
-print(f"Ground joints: {result.ground}")
-print(f"Drivers:       {result.drivers}")
-print(f"Assur groups:  {len(result.groups)}")
+print(f"Ground joints: {result.ground}")
+print(f"Drivers:       {result.drivers}")
+print(f"Assur groups:  {len(result.groups)}")
 for group in result.groups:
-    print(f"  {type(group).__name__} {group.joint_signature}: "
-          f"solves {group.internal_nodes} from {group.anchor_nodes} "
-          f"through links {group.internal_edges}")
+    print(f"  {type(group).__name__} {group.joint_signature}: "
+          f"solves {group.internal_nodes} from {group.anchor_nodes} "
+          f"through links {group.internal_edges}")
 
    
 
    
 
    Expected output:
    
-
    Ground joints: ['A', 'D']
-Drivers:       ['B']
+
    Ground joints: ['A', 'D']
+Drivers:       ['B']
 Assur groups:  1
-  Dyad RRR: solves ('C',) from ('B', 'D') through links ('BC', 'CD')
+  Dyad RRR: solves ('C',) from ('B', 'D') through links ('BC', 'CD')
 
    
 
    
 
    validate_decomposition returns a list of problems — an empty list
@@ -384,7 +384,7 @@ 
    Decomposing a Linkage
 
    from pylinkage.assur import validate_decomposition
 
-print(f"Problems: {validate_decomposition(result)}")
+print(f"Problems: {validate_decomposition(result)}")
 
    
 
    
 
@@ -395,13 +395,13 @@ 
    Converting Graph to Mechanism
    from pylinkage.assur import graph_to_mechanism, mechanism_to_graph
 
 mechanism = graph_to_mechanism(graph, dims)
-print(f"Created mechanism with {len(mechanism.joints)} joints")
+print(f"Created mechanism with {len(mechanism.joints)} joints")
 for joint in mechanism.joints:
-    print(f"  {joint.id}: {type(joint).__name__}")
+    print(f"  {joint.id}: {type(joint).__name__}")
 
 # Back from any Mechanism, e.g. one from MechanismBuilder or synthesis
 graph_back, dims_back = mechanism_to_graph(mechanism)
-print(f"Recovered {len(graph_back.nodes)} nodes, lengths {dims_back.edge_distances}")
+print(f"Recovered {len(graph_back.nodes)} nodes, lengths {dims_back.edge_distances}")
 
    
 
    
 
    Expected output:
    
@@ -410,7 +410,7 @@ 
    Converting Graph to Mechanismedge_0 … and includes the ground
@@ -424,17 +424,17 @@ 
    AssurMechanismassur = AssurMechanism.from_mechanism(fourbar(crank=1.0, coupler=3.0, rocker=3.0, ground=4.0))
 
-print(f"DOF: {assur.degree_of_freedom}")
-print(f"Assur groups: {assur.num_assur_groups}")
-print(f"Valid: {assur.is_valid()}")
-print(f"Group signatures: {[g.joint_signature for g in assur.assur_groups]}")
+print(f"DOF: {assur.degree_of_freedom}")
+print(f"Assur groups: {assur.num_assur_groups}")
+print(f"Valid: {assur.is_valid()}")
+print(f"Group signatures: {[g.joint_signature for g in assur.assur_groups]}")
 
    
 
    
 
    Expected output:
    
 
    DOF: 1
 Assur groups: 1
 Valid: True
-Group signatures: ['RRR']
+Group signatures: ['RRR']
 
    
 
    
 
@@ -446,18 +446,18 @@ 
    Assur Signatures
    from pylinkage.assur import parse_signature, signature_to_hypergraph
 
-signature = parse_signature("RRP")
-print(f"{signature.raw_string}: {signature.group_class.name}, joints {[j.name for j in signature.joints]}")
+signature = parse_signature("RRP")
+print(f"{signature.raw_string}: {signature.group_class.name}, joints {[j.name for j in signature.joints]}")
 
-dyad = signature_to_hypergraph("RRR", prefix="d1_")
-print(f"Nodes: {list(dyad.nodes)}")
-print(f"Edges: {list(dyad.edges)}")
+dyad = signature_to_hypergraph("RRR", prefix="d1_")
+print(f"Nodes: {list(dyad.nodes)}")
+print(f"Edges: {list(dyad.edges)}")
 
    
 
    
 
    Expected output:
    
-
    RRP: DYAD, joints ['REVOLUTE', 'REVOLUTE', 'PRISMATIC']
-Nodes: ['d1_anchor_0', 'd1_anchor_1', 'd1_internal_0']
-Edges: ['d1_link_0', 'd1_link_1']
+
    RRP: DYAD, joints ['REVOLUTE', 'REVOLUTE', 'PRISMATIC']
+Nodes: ['d1_anchor_0', 'd1_anchor_1', 'd1_internal_0']
+Edges: ['d1_link_0', 'd1_link_1']
 
    
 
    
 
@@ -471,13 +471,13 @@ 
    Serializing Linkage Graphsfrom pylinkage.assur import graph_from_json, graph_to_dict, graph_to_json
 
-print(json.dumps(graph_to_dict(graph)["nodes"][0]))
+print(json.dumps(graph_to_dict(graph)["nodes"][0]))
 
 with tempfile.TemporaryDirectory() as tmp:
-    path = Path(tmp) / "fourbar_assur.json"
+    path = Path(tmp) / "fourbar_assur.json"
     graph_to_json(graph, path)
     loaded = graph_from_json(path)
-print(f"Reloaded {len(loaded.nodes)} nodes, {len(loaded.edges)} edges")
+print(f"Reloaded {len(loaded.nodes)} nodes, {len(loaded.edges)} edges")
 
    
 
    
 
    The hypergraph module has the same four functions for HypergraphLinkage
@@ -499,15 +499,15 @@ 
    Mobility Analysis
    from pylinkage.topology import compute_dof, compute_mobility
 
 info = compute_mobility(hg)
-print(f"Links: {info.num_links}, full joints: {info.num_full_joints}, DOF: {info.dof}")
+print(f"Links: {info.num_links}, full joints: {info.num_full_joints}, DOF: {info.dof}")
 
 mobility = compute_dof(hg)
 if mobility == 1:
-    print("Single-DOF mechanism (typical linkage)")
+    print("Single-DOF mechanism (typical linkage)")
 elif mobility == 0:
-    print("Structure (no motion)")
+    print("Structure (no motion)")
 else:
-    print(f"Under-constrained ({mobility} DOF)")
+    print(f"Under-constrained ({mobility} DOF)")
 
    
 
    
 
    Expected output:
    
@@ -518,7 +518,7 @@ 
    Mobility Analysis
    info = compute_mobility(hg_coupler)
-print(f"Coupler four-bar: {info.num_links} links, DOF {info.dof}")
+print(f"Coupler four-bar: {info.num_links} links, DOF {info.dof}")
 
    
 
    
 
    Expected output:
    
@@ -536,18 +536,18 @@ 
    Isomorphism Detection
 
    from pylinkage.topology import are_isomorphic, canonical_hash
 
-other = HypergraphLinkage(name="renamed")
+other = HypergraphLinkage(name="renamed")
 for node_id, role in [
-    ("p", NodeRole.GROUND), ("q", NodeRole.DRIVER), ("r", NodeRole.DRIVEN), ("s", NodeRole.GROUND),
+    ("p", NodeRole.GROUND), ("q", NodeRole.DRIVER), ("r", NodeRole.DRIVEN), ("s", NodeRole.GROUND),
 ]:
     other.add_node(Node(node_id, role=role))
-other.add_edge(Edge("e1", "p", "q"))
-other.add_edge(Edge("e2", "q", "r"))
-other.add_edge(Edge("e3", "r", "s"))
+other.add_edge(Edge("e1", "p", "q"))
+other.add_edge(Edge("e2", "q", "r"))
+other.add_edge(Edge("e3", "r", "s"))
 
-print(f"Same topology: {are_isomorphic(hg, other)}")
-print(f"Same hash: {canonical_hash(hg) == canonical_hash(other)}")
-print(f"Coupler four-bar is a four-bar: {are_isomorphic(hg, hg_coupler)}")
+print(f"Same topology: {are_isomorphic(hg, other)}")
+print(f"Same hash: {canonical_hash(hg) == canonical_hash(other)}")
+print(f"Coupler four-bar is a four-bar: {are_isomorphic(hg, hg_coupler)}")
 
    
 
    
 
    Expected output:
    
@@ -565,15 +565,15 @@ 
    The Topology Catalogcatalog = load_catalog()
 for entry in catalog.by_num_links(6):
-    print(f"{entry.id}: {entry.name}, {entry.num_joints} joints, groups {entry.assur_groups}")
+    print(f"{entry.id}: {entry.name}, {entry.num_joints} joints, groups {entry.assur_groups}")
 
-stephenson = catalog.get("stephenson").to_graph()
-print(f"Stephenson: {len(stephenson.nodes)} nodes, {len(stephenson.hyperedges)} ternary links")
+stephenson = catalog.get("stephenson").to_graph()
+print(f"Stephenson: {len(stephenson.nodes)} nodes, {len(stephenson.hyperedges)} ternary links")
 
    
 
    
 
    Expected output:
    
-
    watt: Watt six-bar, 7 joints, groups ('RRR', 'RRR')
-stephenson: Stephenson six-bar, 7 joints, groups ('RRRRRR',)
+
    watt: Watt six-bar, 7 joints, groups ('RRR', 'RRR')
+stephenson: Stephenson six-bar, 7 joints, groups ('RRRRRR',)
 Stephenson: 7 nodes, 2 ternary links
 
    
 
    
diff --git a/docs/tutorials/index.html b/docs/tutorials/index.html
index edecc0d..cad12cf 100644
--- a/docs/tutorials/index.html
+++ b/docs/tutorials/index.html
@@ -6,14 +6,14 @@
   
 
   
-  Tutorials — pylinkage 1.2.2 documentation
+  Tutorials — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
diff --git a/docs/tutorials/kinematics_optimization.html b/docs/tutorials/kinematics_optimization.html
index 5cc8133..366a3d6 100644
--- a/docs/tutorials/kinematics_optimization.html
+++ b/docs/tutorials/kinematics_optimization.html
@@ -6,14 +6,14 @@
   
 
   
-  Kinematics-Based Optimization — pylinkage 1.2.2 documentation
+  Kinematics-Based Optimization — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -147,12 +147,12 @@ 
    Setting Up Angular Velocityfrom pylinkage.simulation import Linkage
 
 # Create a four-bar linkage
-A = Ground(0.0, 0.0, name="A")
-D = Ground(3.0, 0.0, name="D")
-crank = Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="Crank")
+A = Ground(0.0, 0.0, name="A")
+D = Ground(3.0, 0.0, name="D")
+crank = Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="Crank")
 output = RRRDyad(
     anchor1=crank.output, anchor2=D,
-    distance1=3.0, distance2=2.0, name="Output",
+    distance1=3.0, distance2=2.0, name="Output",
 )
 linkage = Linkage([A, D, crank, output])
 
@@ -181,7 +181,7 @@ 
    Running Kinematics Simulationframe = 25
 for i, component in enumerate(linkage.components):
     vx, vy = velocities[frame, i]
-    print(f"{component.name}: velocity = ({vx:.2f}, {vy:.2f})")
+    print(f"{component.name}: velocity = ({vx:.2f}, {vy:.2f})")
 
    
 
    
 
    Positions the solver could not assemble come out as NaN rather than an
@@ -194,12 +194,12 @@ 
    Querying Joint Velocitiesall_velocities = linkage.get_velocities()
 # Returns: [(vx0, vy0), (vx1, vy1), ...]
 
-# Access an individual component's velocity
+# Access an individual component's velocity
 output_velocity = linkage.components[-1].velocity
 if output_velocity is not None:
     vx, vy = output_velocity
     speed = (vx**2 + vy**2) ** 0.5
-    print(f"Output speed: {speed:.2f} units/s")
+    print(f"Output speed: {speed:.2f} units/s")
 
    
 
    
 
@@ -217,19 +217,19 @@ 
    Example: Minimize Peak Velocitydef create_linkage():
-    A = Ground(0.0, 0.0, name="A")
-    D = Ground(3.0, 0.0, name="D")
-    crank = _Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="Crank")
+    A = Ground(0.0, 0.0, name="A")
+    D = Ground(3.0, 0.0, name="D")
+    crank = _Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="Crank")
     output = RRRDyad(
         anchor1=crank.output, anchor2=D,
-        distance1=3.0, distance2=2.0, name="Output",
+        distance1=3.0, distance2=2.0, name="Output",
     )
     return Linkage([A, D, crank, output])
 
 
 @pl.kinematic_minimization
 def minimize_peak_velocity(loci, linkage=None, **kwargs):
-    """Minimize the peak velocity at the output joint."""
+    """Minimize the peak velocity at the output joint."""
     crank = next(c for c in linkage.components if isinstance(c, _Crank))
     linkage.set_input_velocity(crank, omega=10.0)
 
@@ -242,7 +242,7 @@ 
    Example: Minimize Peak Velocity# Return peak velocity (we want to minimize this)
     peak_velocity = np.nanmax(speeds)
-    return peak_velocity if not np.isnan(peak_velocity) else float('inf')
+    return peak_velocity if not np.isnan(peak_velocity) else float('inf')
 
 
 # Run optimization
@@ -260,8 +260,8 @@ 
    Example: Minimize Peak Velocity)
 
 best = results[0]
-print(f"Minimum peak velocity: {best.score:.2f} units/s")
-print(f"Dimensions: {best.dimensions}")
+print(f"Minimum peak velocity: {best.score:.2f} units/s")
+print(f"Dimensions: {best.dimensions}")
 
    
 
    
 
    The trivial answer to “lowest peak velocity” is a tiny crank, and that is
@@ -273,7 +273,7 @@ 
    Example: Uniform Velocity Profile
    @pl.kinematic_minimization
 def uniform_velocity(loci, linkage=None, **kwargs):
-    """Minimize velocity variation at the output joint."""
+    """Minimize velocity variation at the output joint."""
     crank = next(c for c in linkage.components if isinstance(c, _Crank))
     linkage.set_input_velocity(crank, omega=10.0)
 
@@ -286,7 +286,7 @@ 
    Example: Uniform Velocity Profile# Filter out NaN values
     valid_speeds = speeds[~np.isnan(speeds)]
     if len(valid_speeds) == 0:
-        return float('inf')
+        return float('inf')
 
     # Minimize standard deviation of speed (uniformity measure)
     velocity_variance = np.std(valid_speeds)
@@ -294,7 +294,7 @@ 
    Example: Uniform Velocity Profile# Also penalize very low average speed (we want motion, not stillness)
     avg_speed = np.mean(valid_speeds)
     if avg_speed < 5.0:
-        return float('inf')
+        return float('inf')
 
     return velocity_variance
 
@@ -308,7 +308,7 @@ 
    Example: Uniform Velocity Profileiterations=30,
     verbose=False,
 )
-print(f"Speed standard deviation: {results[0].score:.3f} units/s")
+print(f"Speed standard deviation: {results[0].score:.3f} units/s")
 
    
 
    
 
@@ -317,7 +317,7 @@ 
    Example: Velocity Direction Constraint
    @pl.kinematic_minimization
 def horizontal_velocity(loci, linkage=None, **kwargs):
-    """Maximize horizontal velocity component at output."""
+    """Maximize horizontal velocity component at output."""
     crank = next(c for c in linkage.components if isinstance(c, _Crank))
     linkage.set_input_velocity(crank, omega=10.0)
 
@@ -334,7 +334,7 @@ 
    Example: Velocity Direction Constraint# Filter NaN and calculate average
     valid_ratio = horizontal_ratio[~np.isnan(horizontal_ratio)]
     if len(valid_ratio) == 0:
-        return float('inf')
+        return float('inf')
 
     # Return negative average (we want to maximize horizontal component)
     return -np.mean(valid_ratio)
@@ -349,7 +349,7 @@ 
    Example: Velocity Direction Constraintiterations=30,
     verbose=False,
 )
-print(f"Horizontal fraction of the output velocity: {-results[0].score:.3f}")
+print(f"Horizontal fraction of the output velocity: {-results[0].score:.3f}")
 
    
 
    
 
@@ -359,7 +359,7 @@ 
    Combined Path and Velocity Optimization
    @pl.kinematic_minimization
 def path_and_velocity(loci, linkage=None, **kwargs):
-    """Optimize path shape while limiting peak velocity."""
+    """Optimize path shape while limiting peak velocity."""
     # Path shape objective
     output_path = [step[-1] for step in loci]
     bbox = pl.bounding_box(output_path)
@@ -391,7 +391,7 @@ 
    Combined Path and Velocity Optimizationiterations=30,
     verbose=False,
 )
-print(f"Combined score: {results[0].score:.3f}")
+print(f"Combined score: {results[0].score:.3f}")
 
    
 
    
 
@@ -408,7 +408,7 @@ 
    Matplotlib Visualization# Show single frame with velocity vectors
 fig = show_kinematics(linkage, frame_index=25, show_velocity=True)
-fig.savefig("velocity_frame.png")
+fig.savefig("velocity_frame.png")
 
 # Create animation with velocity vectors (saved as GIF via Pillow)
 fig = animate_kinematics(
@@ -416,7 +416,7 @@ 
    Matplotlib Visualizationshow_velocity=True,
     fps=24,
     duration=2.0,
-    save_path="velocity_animation.gif",
+    save_path="velocity_animation.gif",
 )
 
    
 
    
@@ -430,9 +430,9 @@ 
    Plotly Interactive Visualizationlinkage,
     frame_index=25,
     velocity_scale=0.1,
-    title="Four-bar with Velocity Vectors",
+    title="Four-bar with Velocity Vectors",
 )
-fig.write_html("velocity_plot.html")
+fig.write_html("velocity_plot.html")
 
    
 
    
 
@@ -445,10 +445,10 @@ 
    SVG Publication-Quality Output# Save SVG with velocity vectors
 save_linkage_svg_with_velocity(
     linkage,
-    "linkage_velocity.svg",
+    "linkage_velocity.svg",
     positions[25],
     velocities[25],
-    velocity_color="#0066CC"
+    velocity_color="#0066CC"
 )
 
    
 
    
@@ -470,7 +470,7 @@ 
    Performance Considerationslinkage.set_input_velocity(crank, omega=10.0)
     positions, velocities, accelerations = linkage.step_fast_with_kinematics()
     if np.isnan(positions).any():
-        return float("inf")
+        return float("inf")
 
     # Compute all metrics from the same arrays
     speeds = np.linalg.norm(velocities[:, -1, :], axis=1)
diff --git a/docs/tutorials/multi_objective.html b/docs/tutorials/multi_objective.html
index 08604b9..990cc2f 100644
--- a/docs/tutorials/multi_objective.html
+++ b/docs/tutorials/multi_objective.html
@@ -6,14 +6,14 @@
   
 
   
-  Multi-Objective Optimization — pylinkage 1.2.2 documentation
+  Multi-Objective Optimization — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -161,12 +161,12 @@ 
    Basic Example# Create the linkage
 def create_fourbar():
-    A = Ground(0.0, 0.0, name="A")
-    D = Ground(3.0, 0.0, name="D")
-    crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank")
+    A = Ground(0.0, 0.0, name="A")
+    D = Ground(3.0, 0.0, name="D")
+    crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank")
     output = RRRDyad(
         anchor1=crank.output, anchor2=D,
-        distance1=3.0, distance2=2.0, name="Output",
+        distance1=3.0, distance2=2.0, name="Output",
     )
     return Linkage([A, D, crank, output])
 
@@ -174,7 +174,7 @@ 
    Basic Example# Objective 1: Minimize path error
 @kinematic_minimization
 def path_error(loci, **kwargs):
-    """Distance from output path to target circle."""
+    """Distance from output path to target circle."""
     output_path = [step[-1] for step in loci]
     target_center = (4, 1)
     target_radius = 1.5
@@ -189,7 +189,7 @@ 
    Basic Example# Objective 2: Minimize transmission angle deviation from 90 degrees
 @kinematic_minimization
 def transmission_penalty(loci, linkage=None, **kwargs):
-    """Penalize poor transmission angles (coupler-rocker angle far from 90°)."""
+    """Penalize poor transmission angles (coupler-rocker angle far from 90°)."""
     analysis = linkage.analyze_transmission()
     return analysis.max_deviation
 
@@ -202,14 +202,14 @@ 
    Basic Exampleobjectives=[path_error, transmission_penalty],
     linkage=linkage,
     bounds=bounds,
-    objective_names=["Path Error", "Transmission Penalty"],
+    objective_names=["Path Error", "Transmission Penalty"],
     n_generations=30,
     pop_size=40,
     seed=42,
     verbose=False,
 )
 
-print(f"Found {len(results)} Pareto-optimal solutions")
+print(f"Found {len(results)} Pareto-optimal solutions")
 
    
 
    
 
@@ -220,16 +220,16 @@ 
    Understanding the Pareto Front
    # Iterate over solutions
 for member in results:
-    print(f"Scores: {member.scores}")
-    print(f"Constraints: {member.dimensions}")
+    print(f"Scores: {member.scores}")
+    print(f"Constraints: {member.dimensions}")
 
 # Scores as numpy arrays, one per objective
-print(f"Objectives: {list(results.scores)}")
-path_errors = results.scores["Path Error"]  # shape (n_solutions,)
+print(f"Objectives: {list(results.scores)}")
+path_errors = results.scores["Path Error"]  # shape (n_solutions,)
 
 # Rank along one objective
-most_accurate = results.rank("Path Error")[0]
-print(f"Most accurate path: {most_accurate.scores}")
+most_accurate = results.rank("Path Error")[0]
+print(f"Most accurate path: {most_accurate.scores}")
 
    
 
    
 
    The front’s own tools live on ParetoFront; to_pareto_front()
@@ -240,7 +240,7 @@ 
    Understanding the Pareto Frontscores = pareto.scores_array()
 
 # Number of objectives
-print(f"Objectives: {pareto.n_objectives}")
+print(f"Objectives: {pareto.n_objectives}")
 
    
 
    
 
    
@@ -251,9 +251,9 @@ 
    Pareto Dominancesol_b = pareto[1]
 
 if sol_a.dominates(sol_b):
-    print("Solution A is strictly better than B")
+    print("Solution A is strictly better than B")
 else:
-    print("Solutions are non-dominated (trade-offs)")
+    print("Solutions are non-dominated (trade-offs)")
 
    
 
    
 
@@ -267,11 +267,11 @@ 
    2D Pareto Front# Default 2D plot
 fig = pareto.plot()
-plt.savefig("pareto_front.png")
+plt.savefig("pareto_front.png")
 plt.show()
 
 # Custom styling
-fig = pareto.plot(s=100, alpha=0.8, c='blue')
+fig = pareto.plot(s=100, alpha=0.8, c='blue')
 plt.show()
 
    
 
    
@@ -303,7 +303,7 @@ 
    Filtering Solutions
    # Keep 10 well-distributed solutions
 filtered = pareto.filter(max_solutions=10)
 
-print(f"Reduced from {len(pareto)} to {len(filtered)} solutions")
+print(f"Reduced from {len(pareto)} to {len(filtered)} solutions")
 
    
 
    
 
@@ -314,7 +314,7 @@ 
    Hypervolume Indicatorreference = scores.max(axis=0) * 1.1
 
 hv = pareto.hypervolume(reference_point=reference)
-print(f"Hypervolume: {hv}")
+print(f"Hypervolume: {hv}")
 
    
 
    
 
@@ -326,7 +326,7 @@ 
    Combining with Transmission Analysis
    @kinematic_minimization
 def transmission_objective(loci, linkage=None, **kwargs):
-    """Use built-in transmission analysis."""
+    """Use built-in transmission analysis."""
     analysis = linkage.analyze_transmission()
     # Minimize deviation of the mean from the ideal 90 degrees
     return abs(90 - analysis.mean_angle)
@@ -334,7 +334,7 @@ 
    Combining with Transmission Analysis@kinematic_minimization
 def worst_transmission(loci, linkage=None, **kwargs):
-    """Minimize the worst transmission angle."""
+    """Minimize the worst transmission angle."""
     analysis = linkage.analyze_transmission()
     # Return how far the worst angle is from acceptable range
     if analysis.min_angle < 40:
@@ -349,7 +349,7 @@ 
    Combining with Transmission Analysis
    
 
    @kinematic_minimization
 def compactness(loci, **kwargs):
-    """Minimize mechanism bounding box area."""
+    """Minimize mechanism bounding box area."""
     all_points = [p for step in loci for p in step]
     bbox = pl.bounding_box(all_points)
     width = bbox[1] - bbox[3]  # max_x - min_x
@@ -361,8 +361,8 @@ 
    Three-Objective Exampleobjectives=[path_error, transmission_penalty, compactness],
     linkage=create_fourbar(),
     bounds=bounds,
-    objective_names=["Path Error", "Transmission", "Size"],
-    algorithm="nsga2",
+    objective_names=["Path Error", "Transmission", "Size"],
+    algorithm="nsga2",
     n_generations=30,
     pop_size=40,
     seed=42,
@@ -384,7 +384,7 @@ 
    NSGA-II (Default)objectives=[path_error, transmission_penalty],
     linkage=create_fourbar(),
     bounds=bounds,
-    algorithm="nsga2",  # Default
+    algorithm="nsga2",  # Default
     n_generations=20,
     pop_size=40,
     seed=42,
@@ -401,13 +401,13 @@ 
    NSGA-III
     objectives=[path_error, transmission_penalty, compactness],
     linkage=create_fourbar(),
     bounds=bounds,
-    algorithm="nsga3",
+    algorithm="nsga3",
     n_generations=20,
     pop_size=40,
     seed=42,
     verbose=False,
 )
-print(f"NSGA-III kept {len(results)} solutions")
+print(f"NSGA-III kept {len(results)} solutions")
 
    
 
    
 
diff --git a/docs/tutorials/sensitivity_analysis.html b/docs/tutorials/sensitivity_analysis.html
index 6046457..6dfeb5a 100644
--- a/docs/tutorials/sensitivity_analysis.html
+++ b/docs/tutorials/sensitivity_analysis.html
@@ -6,14 +6,14 @@
   
 
   
-  Sensitivity & Tolerance Analysis — pylinkage 1.2.2 documentation
+  Sensitivity & Tolerance Analysis — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
     
@@ -146,12 +146,12 @@ 
    Basic Setupfrom pylinkage.simulation import Linkage
 
 # Create a four-bar linkage (a crank-rocker: 1 + 3.5 < 3 + 2)
-A = Ground(0.0, 0.0, name="A")
-D = Ground(3.5, 0.0, name="D")
-crank = Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="crank")
+A = Ground(0.0, 0.0, name="A")
+D = Ground(3.5, 0.0, name="D")
+crank = Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="crank")
 coupler = RRRDyad(
     anchor1=crank.output, anchor2=D,
-    distance1=3.0, distance2=2.0, name="coupler",
+    distance1=3.0, distance2=2.0, name="coupler",
 )
 linkage = Linkage([A, D, crank, coupler])
 
    
@@ -169,11 +169,11 @@ 
    Basic Usageanalysis = linkage.analyze_sensitivity(delta=0.01)
 
 # View the most sensitive constraint
-print(f"Most sensitive: {analysis.most_sensitive}")
+print(f"Most sensitive: {analysis.most_sensitive}")
 
 # View all constraints ranked by sensitivity
 for name, sensitivity in analysis.sensitivity_ranking:
-    print(f"  {name}: {sensitivity:.4f}")
+    print(f"  {name}: {sensitivity:.4f}")
 
    
 
    
 
    Output:
    
@@ -205,7 +205,7 @@ 
    Analyzing Specific Output Joints# ...or by component object
 analysis = linkage.analyze_sensitivity(output_joint=crank)
-print(f"Crank path: {analysis.sensitivity_ranking}")
+print(f"Crank path: {analysis.sensitivity_ranking}")
 
    
 
    
 
@@ -217,12 +217,12 @@ 
    Including Transmission Angleinclude_transmission=True,  # the default
 )
 
-print(f"Baseline transmission: {analysis.baseline_transmission:.1f}°")
+print(f"Baseline transmission: {analysis.baseline_transmission:.1f}°")
 
 # Transmission angles for each perturbation
 if analysis.perturbed_transmission is not None:
     for name, trans in zip(analysis.constraint_names, analysis.perturbed_transmission):
-        print(f"  {name}: {trans:.1f}°")
+        print(f"  {name}: {trans:.1f}°")
    @@ -250,9 +250,9 @@

    Basic Usage

    Tolerance analysis uses Monte Carlo simulation to assess manufacturing variability:

    # Define tolerances for each constraint
 tolerances = {
-    "crank_radius": 0.1,     # +/- 0.1 mm
-    "coupler_dist1": 0.2,    # +/- 0.2 mm
-    "coupler_dist2": 0.2,    # +/- 0.2 mm
+    "crank_radius": 0.1,     # +/- 0.1 mm
+    "coupler_dist1": 0.2,    # +/- 0.2 mm
+    "coupler_dist2": 0.2,    # +/- 0.2 mm
 }
 
 # Run Monte Carlo analysis
@@ -263,9 +263,9 @@ 
    Basic Usage
 )
 
 # View statistics
-print(f"Mean deviation: {result.mean_deviation:.4f}")
-print(f"Max deviation:  {result.max_deviation:.4f}")
-print(f"Std deviation:  {result.std_deviation:.4f}")
+print(f"Mean deviation: {result.mean_deviation:.4f}")
+print(f"Max deviation:  {result.max_deviation:.4f}")
+print(f"Std deviation:  {result.std_deviation:.4f}")

    Output:

    @@ -297,8 +297,8 @@

    Visualizing the Tolerance Cloudshow_nominal=True, # Show nominal path as red line alpha=0.1 # Transparency for sample points ) -plt.title("Output Path Tolerance Cloud") -plt.savefig("tolerance_cloud.png", dpi=150) +plt.title("Output Path Tolerance Cloud") +plt.savefig("tolerance_cloud.png", dpi=150) plt.show() @@ -314,11 +314,11 @@

    Selective Tolerance Analysis
    # Only analyze crank radius tolerance
 result = linkage.analyze_tolerance(
-    tolerances={"crank_radius": 0.1},
+    tolerances={"crank_radius": 0.1},
     n_samples=500
 )
 
-print(f"Crank-only max deviation: {result.max_deviation:.4f}")
+print(f"Crank-only max deviation: {result.max_deviation:.4f}")
    @@ -333,7 +333,7 @@

    Sensitivity as Fitness Penalty@pl.kinematic_minimization def robust_linkage(loci, linkage=None, **kwargs): - """Optimize for path shape while minimizing sensitivity.""" + """Optimize for path shape while minimizing sensitivity.""" # Path shape objective: a wide, flat output path output_path = [step[-1] for step in loci] @@ -353,7 +353,7 @@

    Sensitivity as Fitness Penaltyrobust_linkage, linkage, bounds=bounds, order_relation=min, n_particles=10, iterations=10, verbose=False, ) -print(f"Best robust score: {results[0].score:.3f}") +print(f"Best robust score: {results[0].score:.3f}")

    Sensitivity analysis simulates the linkage once per constraint, so this @@ -365,14 +365,14 @@

    Tolerance-Based Constraints
    @pl.kinematic_minimization
 def tolerance_constrained(loci, linkage=None, **kwargs):
-    """Optimize path, rejecting designs with excessive variation."""
+    """Optimize path, rejecting designs with excessive variation."""
 
     # Check tolerance
-    tolerances = {"crank_radius": 0.1, "coupler_dist1": 0.2, "coupler_dist2": 0.2}
+    tolerances = {"crank_radius": 0.1, "coupler_dist1": 0.2, "coupler_dist2": 0.2}
     result = linkage.analyze_tolerance(tolerances, n_samples=100, seed=0)
 
     if result.max_deviation > 0.5:  # Reject if max deviation > 0.5mm
-        return float("inf")
+        return float("inf")
 
     # Path objective: a wide, flat output path
     output_path = [step[-1] for step in loci]
@@ -384,7 +384,7 @@ 
    Tolerance-Based Constraintstolerance_constrained, linkage, bounds=bounds, order_relation=min,
     n_particles=10, iterations=10, verbose=False,
 )
-print(f"Best tolerance-constrained score: {results[0].score:.3f}")
+print(f"Best tolerance-constrained score: {results[0].score:.3f}")

    Returning inf (or -inf under @kinematic_maximization) is how a @@ -434,51 +434,51 @@

    Example Complete Workflowfrom pylinkage.simulation import Linkage # Create linkage -A = Ground(0.0, 0.0, name="A") -D = Ground(3.5, 0.0, name="D") -crank = Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="crank") +A = Ground(0.0, 0.0, name="A") +D = Ground(3.5, 0.0, name="D") +crank = Crank(anchor=A, radius=1.0, angular_velocity=0.1, name="crank") coupler = RRRDyad( anchor1=crank.output, anchor2=D, - distance1=3.0, distance2=2.0, name="coupler", + distance1=3.0, distance2=2.0, name="coupler", ) linkage = Linkage([A, D, crank, coupler]) # Step 1: Sensitivity analysis -print("=== Sensitivity Analysis ===") +print("=== Sensitivity Analysis ===") sens = linkage.analyze_sensitivity(delta=0.01) -print(f"Most sensitive: {sens.most_sensitive}") +print(f"Most sensitive: {sens.most_sensitive}") for name, val in sens.sensitivity_ranking: - print(f" {name}: {val:.4f}") + print(f" {name}: {val:.4f}") # Step 2: Tolerance analysis with realistic tolerances -print("\n=== Tolerance Analysis ===") +print("\n=== Tolerance Analysis ===") tolerances = { - "crank_radius": 0.05, # Tight tolerance (sensitive) - "coupler_dist1": 0.1, # Normal tolerance - "coupler_dist2": 0.1, # Normal tolerance + "crank_radius": 0.05, # Tight tolerance (sensitive) + "coupler_dist1": 0.1, # Normal tolerance + "coupler_dist2": 0.1, # Normal tolerance } tol = linkage.analyze_tolerance(tolerances, n_samples=500, seed=42) -print(f"Mean deviation: {tol.mean_deviation:.4f}") -print(f"Max deviation: {tol.max_deviation:.4f}") -print(f"Std deviation: {tol.std_deviation:.4f}") +print(f"Mean deviation: {tol.mean_deviation:.4f}") +print(f"Max deviation: {tol.max_deviation:.4f}") +print(f"Std deviation: {tol.std_deviation:.4f}") # Step 3: Visualize fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6)) # Plot tolerance cloud tol.plot_cloud(ax=ax1) -ax1.set_title("Tolerance Cloud") +ax1.set_title("Tolerance Cloud") # Plot per-position std ax2.plot(tol.position_std) -ax2.set_xlabel("Simulation Step") -ax2.set_ylabel("Position Std Dev") -ax2.set_title("Per-Position Variation") +ax2.set_xlabel("Simulation Step") +ax2.set_ylabel("Position Std Dev") +ax2.set_title("Per-Position Variation") ax2.grid(True) plt.tight_layout() -plt.savefig("tolerance_analysis.png", dpi=150) +plt.savefig("tolerance_analysis.png", dpi=150) plt.show() diff --git a/docs/tutorials/symbolic.html b/docs/tutorials/symbolic.html index 97cb2bd..5cae355 100644 --- a/docs/tutorials/symbolic.html +++ b/docs/tutorials/symbolic.html @@ -6,14 +6,14 @@ - Symbolic Computation — pylinkage 1.2.2 documentation + Symbolic Computation — pylinkage 1.3.0 documentation - + @@ -183,18 +183,18 @@

    Quick Start# Create a four-bar with symbolic parameters linkage = fourbar_symbolic( ground_length=4, # Fixed: distance between ground pivots - crank_length="L1", # Symbolic: input crank length - coupler_length="L2", # Symbolic: coupler bar length - rocker_length="L3", # Symbolic: output rocker length + crank_length="L1", # Symbolic: input crank length + coupler_length="L2", # Symbolic: coupler bar length + rocker_length="L3", # Symbolic: output rocker length ) # Get closed-form trajectory expressions solutions = solve_linkage_symbolically(linkage) # Print the crank position (simple expression) -x_crank, y_crank = solutions["B"] -print(f"Crank x: {x_crank}") -print(f"Crank y: {y_crank}") +x_crank, y_crank = solutions["B"] +print(f"Crank x: {x_crank}") +print(f"Crank y: {y_crank}")

    Output:

    @@ -233,22 +233,22 @@

    Illustrated Example: Effect of Link Lengthslinkage = fourbar_symbolic( ground_length=4, - crank_length="L1", - coupler_length="L2", - rocker_length="L3", + crank_length="L1", + coupler_length="L2", + rocker_length="L3", ) theta_vals = np.linspace(0, 2*np.pi, 360) # Compare different crank lengths for L1 in [0.5, 1.0, 1.5]: - params = {"L1": L1, "L2": 3.0, "L3": 3.0} + params = {"L1": L1, "L2": 3.0, "L3": 3.0} traj = compute_trajectory_numeric(linkage, params, theta_vals) - output = traj["C"] + output = traj["C"] x_range = np.ptp(output[:, 0]) # peak-to-peak y_range = np.ptp(output[:, 1]) - print(f"L1={L1}: X range={x_range:.3f}, Y range={y_range:.3f}") + print(f"L1={L1}: X range={x_range:.3f}, Y range={y_range:.3f}")

    Output:

    @@ -273,28 +273,28 @@

    Method 1: fourbar_symbolic (Recommended)coupler_length=3, rocker_length=3, ) -print(f"Parameters: {list(linkage1.parameters.keys())}") +print(f"Parameters: {list(linkage1.parameters.keys())}") # Output: Parameters: [] (no symbolic parameters) # Mixed symbolic/numeric - for optimization linkage2 = fourbar_symbolic( ground_length=4, # Fixed - crank_length="L1", # Optimize this - coupler_length="L2", # Optimize this + crank_length="L1", # Optimize this + coupler_length="L2", # Optimize this rocker_length=3, # Fixed ) -print(f"Parameters: {list(linkage2.parameters.keys())}") -# Output: Parameters: ['L1', 'L2'] +print(f"Parameters: {list(linkage2.parameters.keys())}") +# Output: Parameters: ['L1', 'L2'] # All symbolic - for general analysis linkage3 = fourbar_symbolic( - ground_length="L0", - crank_length="L1", - coupler_length="L2", - rocker_length="L3", + ground_length="L0", + crank_length="L1", + coupler_length="L2", + rocker_length="L3", ) -print(f"Parameters: {list(linkage3.parameters.keys())}") -# Output: Parameters: ['L0', 'L1', 'L2', 'L3'] +print(f"Parameters: {list(linkage3.parameters.keys())}") +# Output: Parameters: ['L0', 'L1', 'L2', 'L3'] @@ -307,18 +307,18 @@

    Method 2: Building from SymJoint Classesimport sympy as sp # Define symbolic parameters -L1, L2, L3 = sp.symbols('L1 L2 L3', positive=True, real=True) +L1, L2, L3 = sp.symbols('L1 L2 L3', positive=True, real=True) # Create joints in order -ground_A = SymStatic(x=0, y=0, name="A") -ground_D = SymStatic(x=4, y=0, name="D") -crank_B = SymCrank(parent=ground_A, radius=L1, name="B") +ground_A = SymStatic(x=0, y=0, name="A") +ground_D = SymStatic(x=4, y=0, name="D") +crank_B = SymCrank(parent=ground_A, radius=L1, name="B") coupler_C = SymRevolute( parent0=crank_B, parent1=ground_D, distance0=L2, distance1=L3, - name="C" + name="C" ) # Assemble linkage @@ -326,8 +326,8 @@

    Method 2: Building from SymJoint Classesjoints=[ground_A, ground_D, crank_B, coupler_C] ) -print(f"Joints: {[j.name for j in linkage.joints]}") -# Output: Joints: ['A', 'D', 'B', 'C'] +print(f"Joints: {[j.name for j in linkage.joints]}") +# Output: Joints: ['A', 'D', 'B', 'C'] @@ -346,12 +346,12 @@

    Reading Back Numeric Valuesrocker_length=3.0, ) -print(f"Parameters: {list(linkage.parameters.keys())}") +print(f"Parameters: {list(linkage.parameters.keys())}") # If you populated ``_numeric_*`` attributes on each SymJoint, they # are surfaced back out here. values = get_numeric_parameters(linkage) -print(f"Current numeric values: {values}") +print(f"Current numeric values: {values}") @@ -366,13 +366,13 @@

    Numeric Evaluationlinkage = fourbar_symbolic( ground_length=4, - crank_length="L1", - coupler_length="L2", - rocker_length="L3", + crank_length="L1", + coupler_length="L2", + rocker_length="L3", ) # Define parameter values -params = {"L1": 1.0, "L2": 3.0, "L3": 3.0} +params = {"L1": 1.0, "L2": 3.0, "L3": 3.0} # Compute trajectory over full rotation theta_values = np.linspace(0, 2 * np.pi, 100) @@ -380,12 +380,12 @@

    Numeric Evaluation# Results are returned as a dictionary # Each joint maps to an (N, 2) array of [x, y] positions -coupler = trajectories["C"] +coupler = trajectories["C"] -print(f"Shape: {coupler.shape}") -print(f"Start: ({coupler[0, 0]:.3f}, {coupler[0, 1]:.3f})") -print(f"At 90 deg: ({coupler[25, 0]:.3f}, {coupler[25, 1]:.3f})") -print(f"At 180 deg: ({coupler[50, 0]:.3f}, {coupler[50, 1]:.3f})") +print(f"Shape: {coupler.shape}") +print(f"Start: ({coupler[0, 0]:.3f}, {coupler[0, 1]:.3f})") +print(f"At 90 deg: ({coupler[25, 0]:.3f}, {coupler[25, 1]:.3f})") +print(f"At 180 deg: ({coupler[50, 0]:.3f}, {coupler[50, 1]:.3f})")

    Output:

    @@ -412,7 +412,7 @@

    Fast Pre-Compiled Functionsfuncs = create_trajectory_functions(linkage) # Each joint has (x_func, y_func, param_symbols) -x_func, y_func, params = funcs["C"] +x_func, y_func, params = funcs["C"] # Time comparison from pylinkage.symbolic import compute_trajectory_numeric @@ -430,9 +430,9 @@

    Fast Pre-Compiled Functionsy_func(theta_vals) compiled_time = time.perf_counter() - start -print(f"Direct: {direct_time:.3f}s") -print(f"Compiled: {compiled_time:.3f}s") -print(f"Speedup: {direct_time/compiled_time:.1f}x") +print(f"Direct: {direct_time:.3f}s") +print(f"Compiled: {compiled_time:.3f}s") +print(f"Speedup: {direct_time/compiled_time:.1f}x")

    Output:

    @@ -465,19 +465,19 @@

    Understanding SymbolicOptimizerlinkage = fourbar_symbolic( ground_length=4, - crank_length="L1", - coupler_length="L2", - rocker_length="L3", + crank_length="L1", + coupler_length="L2", + rocker_length="L3", ) # Symbolic objective: minimize squared distance to point (3, 1.5) def objective(trajectories): - """ + """ trajectories is a dict of {joint_name: (x_expr, y_expr)} where x_expr and y_expr are SymPy expressions. Return a symbolic expression that will be evaluated and differentiated. - """ - x, y = trajectories["C"] # SymPy expressions + """ + x, y = trajectories["C"] # SymPy expressions target_x, target_y = 3.0, 1.5 return (x - target_x)**2 + (y - target_y)**2 @@ -486,16 +486,16 @@

    Understanding SymbolicOptimizer# Run optimization result = optimizer.optimize( - initial_params={"L1": 1.0, "L2": 3.0, "L3": 3.0}, - bounds={"L1": (0.3, 2.0), "L2": (1.5, 5.0), "L3": (1.5, 5.0)}, + initial_params={"L1": 1.0, "L2": 3.0, "L3": 3.0}, + bounds={"L1": (0.3, 2.0), "L2": (1.5, 5.0), "L3": (1.5, 5.0)}, ) -print(f"Success: {result.success}") -print(f"Iterations: {result.iterations}") -print(f"Optimal L1: {result.params['L1']:.4f}") -print(f"Optimal L2: {result.params['L2']:.4f}") -print(f"Optimal L3: {result.params['L3']:.4f}") -print(f"Final objective: {result.objective_value:.6f}") +print(f"Success: {result.success}") +print(f"Iterations: {result.iterations}") +print(f"Optimal L1: {result.params['L1']:.4f}") +print(f"Optimal L2: {result.params['L2']:.4f}") +print(f"Optimal L3: {result.params['L3']:.4f}") +print(f"Final objective: {result.objective_value:.6f}")

    Output:

    @@ -519,17 +519,17 @@

    Verifying Results# Initial trajectory initial_traj = compute_trajectory_numeric( - linkage, {"L1": 1.0, "L2": 3.0, "L3": 3.0}, theta_vals + linkage, {"L1": 1.0, "L2": 3.0, "L3": 3.0}, theta_vals ) -initial_dist = np.mean(np.sqrt(np.sum((initial_traj["C"] - target)**2, axis=1))) +initial_dist = np.mean(np.sqrt(np.sum((initial_traj["C"] - target)**2, axis=1))) # Optimized trajectory optimal_traj = compute_trajectory_numeric(linkage, result.params, theta_vals) -optimal_dist = np.mean(np.sqrt(np.sum((optimal_traj["C"] - target)**2, axis=1))) +optimal_dist = np.mean(np.sqrt(np.sum((optimal_traj["C"] - target)**2, axis=1))) -print(f"Initial mean distance: {initial_dist:.4f}") -print(f"Optimal mean distance: {optimal_dist:.4f}") -print(f"Improvement: {(1 - optimal_dist/initial_dist)*100:.1f}%") +print(f"Initial mean distance: {initial_dist:.4f}") +print(f"Optimal mean distance: {optimal_dist:.4f}") +print(f"Improvement: {(1 - optimal_dist/initial_dist)*100:.1f}%")

    Output:

    @@ -544,13 +544,13 @@

    Example Objective Functions
    def point_distance_objective(trajectories):
-    x, y = trajectories["C"]
+    x, y = trajectories["C"]
     return (x - 3.0)**2 + (y - 1.5)**2

    Maximize y-coordinate:

    def maximize_height(trajectories):
-    x, y = trajectories["C"]
+    x, y = trajectories["C"]
     return -y  # Negative because optimizer minimizes
    @@ -559,7 +559,7 @@

    Example Objective Functionsimport sympy as sp def minimize_curvature(trajectories): - x, y = trajectories["C"] + x, y = trajectories["C"] # Second derivatives indicate curvature d2x = sp.diff(x, theta, 2) d2y = sp.diff(y, theta, 2) @@ -581,19 +581,19 @@

    Computing Sensitivitylinkage = fourbar_symbolic( ground_length=4, - crank_length="L1", - coupler_length="L2", - rocker_length="L3", + crank_length="L1", + coupler_length="L2", + rocker_length="L3", ) # Get symbolic expressions solutions = solve_linkage_symbolically(linkage) -x_coupler, y_coupler = solutions["C"] +x_coupler, y_coupler = solutions["C"] -# Differentiate with respect to the linkage's own symbols. A fresh -# sp.symbols("L1 L2 L3") would carry different assumptions, count as +# Differentiate with respect to the linkage's own symbols. A fresh +# sp.symbols("L1 L2 L3") would carry different assumptions, count as # unrelated symbols, and give zero gradients. -L1, L2, L3 = (linkage.parameters[name] for name in ("L1", "L2", "L3")) +L1, L2, L3 = (linkage.parameters[name] for name in ("L1", "L2", "L3")) params = [L1, L2, L3] # Compute gradients (sensitivity) @@ -603,10 +603,10 @@

    Computing Sensitivity# Evaluate at a specific configuration values = {L1: 1.0, L2: 3.0, L3: 3.0, theta: 0} -print("Sensitivity of coupler x-position:") +print("Sensitivity of coupler x-position:") for param, g in zip(params, grad_x): sensitivity = float(g.subs(values).evalf()) - print(f" dx/d{param} = {sensitivity:.4f}") + print(f" dx/d{param} = {sensitivity:.4f}") @@ -617,21 +617,21 @@

    Tolerance Analysis Exampleimport numpy as np linkage = fourbar_symbolic( - ground_length=4, crank_length="L1", - coupler_length="L2", rocker_length="L3" + ground_length=4, crank_length="L1", + coupler_length="L2", rocker_length="L3" ) # Nominal parameters -nominal = {"L1": 1.0, "L2": 3.0, "L3": 3.0} +nominal = {"L1": 1.0, "L2": 3.0, "L3": 3.0} tolerance = 0.1 # +/- 0.1 manufacturing tolerance theta_vals = np.linspace(0, 2*np.pi, 100) nominal_traj = compute_trajectory_numeric(linkage, nominal, theta_vals) -print("Effect of +0.1 tolerance on each parameter:") -print("-" * 50) +print("Effect of +0.1 tolerance on each parameter:") +print("-" * 50) -for param in ["L1", "L2", "L3"]: +for param in ["L1", "L2", "L3"]: perturbed = nominal.copy() perturbed[param] += tolerance @@ -639,11 +639,11 @@

    Tolerance Analysis Example# Maximum deviation from nominal deviation = np.max(np.sqrt( - (nominal_traj["C"][:, 0] - perturbed_traj["C"][:, 0])**2 + - (nominal_traj["C"][:, 1] - perturbed_traj["C"][:, 1])**2 + (nominal_traj["C"][:, 0] - perturbed_traj["C"][:, 0])**2 + + (nominal_traj["C"][:, 1] - perturbed_traj["C"][:, 1])**2 )) - print(f" {param}: max deviation = {deviation:.4f}") + print(f" {param}: max deviation = {deviation:.4f}")

    Output:

    @@ -715,21 +715,21 @@

    Converting Back to Numeric# Create symbolic linkage for analysis / gradient-based optimisation sym_linkage = fourbar_symbolic( ground_length=4, - crank_length="L1", - coupler_length="L2", - rocker_length="L3", + crank_length="L1", + coupler_length="L2", + rocker_length="L3", ) # Optimal parameters from symbolic optimisation -optimal_params = {"L1": 0.3, "L2": 3.36, "L3": 1.82} +optimal_params = {"L1": 0.3, "L2": 3.36, "L3": 1.82} # Rebuild the four-bar numerically with those parameters. -A = Ground(0.0, 0.0, name="A") -D = Ground(4.0, 0.0, name="D") -crank = Crank(anchor=A, radius=optimal_params["L1"], angular_velocity=0.1) +A = Ground(0.0, 0.0, name="A") +D = Ground(4.0, 0.0, name="D") +crank = Crank(anchor=A, radius=optimal_params["L1"], angular_velocity=0.1) output = RRRDyad( anchor1=crank.output, anchor2=D, - distance1=optimal_params["L2"], distance2=optimal_params["L3"], + distance1=optimal_params["L2"], distance2=optimal_params["L3"], ) numeric_linkage = Linkage([A, D, crank, output]) @@ -750,14 +750,14 @@

    Converting Back to Numericfitness, numeric_linkage, bounds=bounds, order_relation=min, n_particles=20, iterations=20, verbose=False, ) -print(f"PSO fine-tuning: {results[0].score:.4f}") +print(f"PSO fine-tuning: {results[0].score:.4f}")

    Complete Workflow Example

    Here’s a complete example showing the symbolic workflow:

    -
    """Complete symbolic analysis and optimization workflow."""
+
    """Complete symbolic analysis and optimization workflow."""
 from pylinkage.actuators import Crank
 from pylinkage.components import Ground
 from pylinkage.dyads import RRRDyad
@@ -771,68 +771,68 @@ 
    Complete Workflow Exampleimport numpy as np
 
 # Step 1: Create symbolic linkage
-print("Step 1: Create symbolic linkage")
+print("Step 1: Create symbolic linkage")
 linkage = fourbar_symbolic(
     ground_length=4,
-    crank_length="L1",
-    coupler_length="L2",
-    rocker_length="L3",
+    crank_length="L1",
+    coupler_length="L2",
+    rocker_length="L3",
 )
-print(f"  Parameters: {list(linkage.parameters.keys())}")
+print(f"  Parameters: {list(linkage.parameters.keys())}")
 
 # Step 2: Explore parameter space
-print("\nStep 2: Parameter exploration")
+print("\nStep 2: Parameter exploration")
 theta_vals = np.linspace(0, 2*np.pi, 100)
 
 configs = [
-    {"L1": 0.5, "L2": 3.0, "L3": 3.0},
-    {"L1": 1.0, "L2": 3.0, "L3": 3.0},
-    {"L1": 1.5, "L2": 3.0, "L3": 3.0},
+    {"L1": 0.5, "L2": 3.0, "L3": 3.0},
+    {"L1": 1.0, "L2": 3.0, "L3": 3.0},
+    {"L1": 1.5, "L2": 3.0, "L3": 3.0},
 ]
 
 for params in configs:
     traj = compute_trajectory_numeric(linkage, params, theta_vals)
-    area = np.ptp(traj["C"][:, 0]) * np.ptp(traj["C"][:, 1])
-    print(f"  L1={params['L1']}: workspace area = {area:.3f}")
+    area = np.ptp(traj["C"][:, 0]) * np.ptp(traj["C"][:, 1])
+    print(f"  L1={params['L1']}: workspace area = {area:.3f}")
 
 # Step 3: Optimize
-print("\nStep 3: Gradient-based optimization")
+print("\nStep 3: Gradient-based optimization")
 
 def objective(trajectories):
-    x, y = trajectories["C"]
+    x, y = trajectories["C"]
     return (x - 3.0)**2 + (y - 1.5)**2
 
 optimizer = SymbolicOptimizer(linkage, objective)
 result = optimizer.optimize(
-    initial_params={"L1": 1.0, "L2": 3.0, "L3": 3.0},
-    bounds={"L1": (0.3, 2.0), "L2": (1.5, 5.0), "L3": (1.5, 5.0)},
+    initial_params={"L1": 1.0, "L2": 3.0, "L3": 3.0},
+    bounds={"L1": (0.3, 2.0), "L2": (1.5, 5.0), "L3": (1.5, 5.0)},
 )
 
-print(f"  Success: {result.success}")
-print(f"  Iterations: {result.iterations}")
-print(f"  Optimal: L1={result.params['L1']:.3f}, "
-      f"L2={result.params['L2']:.3f}, L3={result.params['L3']:.3f}")
+print(f"  Success: {result.success}")
+print(f"  Iterations: {result.iterations}")
+print(f"  Optimal: L1={result.params['L1']:.3f}, "
+      f"L2={result.params['L2']:.3f}, L3={result.params['L3']:.3f}")
 
 # Step 4: Build a numeric linkage from the optimised parameters.
-print("\nStep 4: Convert to numeric and visualize")
-A = Ground(0.0, 0.0, name="A")
-D = Ground(4.0, 0.0, name="D")
+print("\nStep 4: Convert to numeric and visualize")
+A = Ground(0.0, 0.0, name="A")
+D = Ground(4.0, 0.0, name="D")
 numeric_crank = Crank(
-    anchor=A, radius=result.params["L1"], angular_velocity=0.1,
+    anchor=A, radius=result.params["L1"], angular_velocity=0.1,
 )
 numeric_output = RRRDyad(
     anchor1=numeric_crank.output, anchor2=D,
-    distance1=result.params["L2"], distance2=result.params["L3"],
+    distance1=result.params["L2"], distance2=result.params["L3"],
 )
 numeric = Linkage([A, D, numeric_crank, numeric_output])
-print(f"  Numeric linkage created with {len(numeric.components)} components")
+print(f"  Numeric linkage created with {len(numeric.components)} components")
 
 # pl.show_linkage(numeric)  # Uncomment to visualize
 
    
 
    
 
    Output:
    
 
    Step 1: Create symbolic linkage
-  Parameters: ['L1', 'L2', 'L3']
+  Parameters: ['L1', 'L2', 'L3']
 
 Step 2: Parameter exploration
   L1=0.5: workspace area = 0.355
diff --git a/docs/tutorials/synthesis.html b/docs/tutorials/synthesis.html
index 9a8a06a..d00ac89 100644
--- a/docs/tutorials/synthesis.html
+++ b/docs/tutorials/synthesis.html
@@ -6,14 +6,14 @@
   
 
   
-  Linkage Synthesis — pylinkage 1.2.2 documentation
+  Linkage Synthesis — pylinkage 1.3.0 documentation
       
       
 
   
       
       
-      
+      
       
       
       
@@ -163,7 +163,7 @@ 
    Quick Start: Path Generation# Find linkages that achieve this path
 result = path_generation(precision_points)
 
-print(f"Found {len(result.solutions)} candidate solutions")
+print(f"Found {len(result.solutions)} candidate solutions")
 
 # Visualize the first solution
 if result.solutions:
@@ -191,7 +191,7 @@ 
    Animating a Solutiondef show(result, index=0):
-    """Animate one solution, oscillating the crank when it cannot turn fully."""
+    """Animate one solution, oscillating the crank when it cannot turn fully."""
     raw = result.raw_solutions[index]
     limits = crank_angle_limits(
         raw.crank_length, raw.coupler_length, raw.rocker_length, raw.ground_length
@@ -199,7 +199,7 @@ 
    Animating a Solutionlinkage = result.solutions[index]
     if limits is not None:
         lo, hi = (math.degrees(a) for a in limits)
-        print(f"crank oscillates between {lo:.1f} and {hi:.1f} deg")
+        print(f"crank oscillates between {lo:.1f} and {hi:.1f} deg")
         linkage = solution_to_linkage(raw._replace(arc_limits=limits), name=linkage.name)
     pl.show_linkage(linkage)
 
@@ -247,21 +247,21 @@ 
    Example: Three Precision Pointsresult = function_generation(angle_pairs, ground_length=2.0)
 
 if result.solutions:
-    print(f"Found {len(result.solutions)} solutions")
+    print(f"Found {len(result.solutions)} solutions")
     for i, sol in enumerate(result.raw_solutions):
-        print(f"\nSolution {i + 1}:")
-        print(f"  Crank length (L1):   {sol.crank_length:.4f}")
-        print(f"  Coupler length (L2): {sol.coupler_length:.4f}")
-        print(f"  Rocker length (L3):  {sol.rocker_length:.4f}")
-        print(f"  Ground length (L4):  {sol.ground_length:.4f}")
+        print(f"\nSolution {i + 1}:")
+        print(f"  Crank length (L1):   {sol.crank_length:.4f}")
+        print(f"  Coupler length (L2): {sol.coupler_length:.4f}")
+        print(f"  Rocker length (L3):  {sol.rocker_length:.4f}")
+        print(f"  Ground length (L4):  {sol.ground_length:.4f}")
 
     # Visualize the first solution
     linkage = result.solutions[0]
     show(result)
 else:
-    print("No valid solutions found")
+    print("No valid solutions found")
     for warning in result.warnings:
-        print(f"Warning: {warning}")
+        print(f"Warning: {warning}")
 
    
 
    
 
    Expected output:
    
@@ -296,10 +296,10 @@ 
    Verifying Function Generation# Check if synthesized linkage achieves the angle pairs
 is_valid, errors = verify_function_generation(linkage, angle_pairs)
 
-print(f"Verification {'passed' if is_valid else 'failed'}:")
+print(f"Verification {'passed' if is_valid else 'failed'}:")
 for i, ((phi, psi), error) in enumerate(zip(angle_pairs, errors)):
-    print(f"  Point {i+1}: phi={math.degrees(phi):.1f}°, "
-          f"psi={math.degrees(psi):.1f}°, error={math.degrees(error):.4f}°")
+    print(f"  Point {i+1}: phi={math.degrees(phi):.1f}°, "
+          f"psi={math.degrees(psi):.1f}°, error={math.degrees(error):.4f}°")
    @@ -331,24 +331,24 @@

    Basic Path Generationresult = path_generation(points, max_solutions=3) -print(f"Found {len(result.solutions)} solutions") -print(f"Warnings: {result.warnings}") +print(f"Found {len(result.solutions)} solutions") +print(f"Warnings: {result.warnings}") # Examine each solution for i, (linkage, raw) in enumerate(zip(result.solutions, result.raw_solutions)): - print(f"\nSolution {i + 1}:") + print(f"\nSolution {i + 1}:") # Link lengths from the raw solution - print(f" Crank {raw.crank_length:.3f}, coupler {raw.coupler_length:.3f}, " - f"rocker {raw.rocker_length:.3f}, ground {raw.ground_length:.3f}") - # The Linkage's own constraints: crank radius, the two RRRDyad - # distances, then the coupler point's distance and angle + print(f" Crank {raw.crank_length:.3f}, coupler {raw.coupler_length:.3f}, " + f"rocker {raw.rocker_length:.3f}, ground {raw.ground_length:.3f}") + # The Linkage's own constraints: crank radius, the two RRRDyad + # distances, then the coupler point's distance and angle constraints = [round(float(c), 3) for c in linkage.get_constraints()] - print(f" Constraints: {constraints}") + print(f" Constraints: {constraints}")

    Example result (may vary):

    Found 3 solutions
-Warnings: ['299 candidate(s) rejected: coupler point did not pass through all precision points (assembly-mode mismatch).']
+Warnings: ['299 candidate(s) rejected: coupler point did not pass through all precision points (assembly-mode mismatch).']
 
 Solution 1:
   Crank 3.843, coupler 4.560, rocker 1.799, ground 0.770
@@ -372,7 +372,7 @@ 
    Path Generation with Timingresult = path_generation_with_timing(points, crank_angles)
 
 if result.solutions:
-    print(f"Found {len(result.solutions)} timed solutions")
+    print(f"Found {len(result.solutions)} timed solutions")
    @@ -403,13 +403,13 @@

    Three-Pose Synthesisresult = motion_generation(poses) -print(f"Found {len(result.solutions)} solutions") +print(f"Found {len(result.solutions)} solutions") if result.solutions: linkage = result.solutions[0] - print("\nLinkage configuration:") + print("\nLinkage configuration:") for component in linkage.components: - print(f" {component.name}: ({component.x:.2f}, {component.y:.2f})") + print(f" {component.name}: ({component.x:.2f}, {component.y:.2f})") show(result) @@ -442,16 +442,16 @@

    Four-Pose and Five-Pose SynthesisPose(3.0, 0.6, 0.6), ] -# With four poses the circle points reduce to Burmester's curve, with +# With four poses the circle points reduce to Burmester's curve, with # five to at most four Burmester points; motion_generation handles both. result = motion_generation(poses) if result.solutions: - print(f"Found {len(result.solutions)} solutions") + print(f"Found {len(result.solutions)} solutions") else: - print("No solution; five poses in particular are often unreachable") + print("No solution; five poses in particular are often unreachable") for warning in result.warnings: - print(f" {warning}") + print(f" {warning}") @@ -465,10 +465,10 @@

    Working with Synthesis Results# Check if solutions were found if result.solutions: - print("Solutions found!") + print("Solutions found!") # Number of solutions -print(f"Count: {len(result.solutions)}") +print(f"Count: {len(result.solutions)}") # Iterate over linkages for linkage in result.solutions: @@ -477,20 +477,20 @@

    Working with Synthesis Results# Or take them as an Ensemble: batch simulation, ranking by link # lengths, filtering, and visualization in one object ensemble = result.ensemble -print(f"{ensemble.n_members} members, scores {list(ensemble.scores)}") -shortest_crank = ensemble.rank("crank_length")[0] -print(f"Shortest crank: {shortest_crank.scores['crank_length']:.3f}") +print(f"{ensemble.n_members} members, scores {list(ensemble.scores)}") +shortest_crank = ensemble.rank("crank_length")[0] +print(f"Shortest crank: {shortest_crank.scores['crank_length']:.3f}") # Access the underlying solutions with full parameters for sol in result.raw_solutions: - print(f"Crank: {sol.crank_length}") - print(f"Coupler: {sol.coupler_length}") - print(f"Rocker: {sol.rocker_length}") - print(f"Ground: {sol.ground_length}") + print(f"Crank: {sol.crank_length}") + print(f"Coupler: {sol.coupler_length}") + print(f"Rocker: {sol.rocker_length}") + print(f"Ground: {sol.ground_length}") # Check for warnings for warning in result.warnings: - print(f"Warning: {warning}") + print(f"Warning: {warning}") @@ -511,10 +511,10 @@

    Creating Linkages from Dimensionsfrom pylinkage.synthesis import grashof_check, is_crank_rocker grashof = grashof_check(1.0, 3.0, 3.0, 4.0) -print(f"Grashof type: {grashof.name}") +print(f"Grashof type: {grashof.name}") if is_crank_rocker(1.0, 3.0, 3.0, 4.0): - print("This is a crank-rocker mechanism") + print("This is a crank-rocker mechanism") pl.show_linkage(linkage) @@ -542,23 +542,23 @@

    Grashof AnalysisL1, L2, L3, L4 = 1.0, 3.0, 3.0, 4.0 # Check if Grashof (shortest + longest <= sum of other two) -print(f"Is Grashof: {is_grashof(L1, L2, L3, L4)}") +print(f"Is Grashof: {is_grashof(L1, L2, L3, L4)}") # Get specific type grashof_type = grashof_check(L1, L2, L3, L4) if grashof_type == GrashofType.GRASHOF_CRANK_ROCKER: - print("Crank makes full rotations, rocker oscillates") + print("Crank makes full rotations, rocker oscillates") elif grashof_type == GrashofType.GRASHOF_DOUBLE_CRANK: - print("Both crank and rocker make full rotations") + print("Both crank and rocker make full rotations") elif grashof_type == GrashofType.GRASHOF_ROCKER_CRANK: - print("Rocker makes full rotations, crank oscillates") + print("Rocker makes full rotations, crank oscillates") elif grashof_type == GrashofType.GRASHOF_DOUBLE_ROCKER: - print("Coupler makes full rotations, crank and rocker oscillate") + print("Coupler makes full rotations, crank and rocker oscillate") elif grashof_type == GrashofType.CHANGE_POINT: - print("Change-point mechanism (special case)") + print("Change-point mechanism (special case)") else: - print("Non-Grashof: no link can rotate fully") + print("Non-Grashof: no link can rotate fully") @@ -581,18 +581,18 @@

    Advanced: Burmester Curve Analysis# Compute relative rotation poles between poses, as complex numbers poles = compute_all_poles(poses) -print(f"Poles: {poles}") +print(f"Poles: {poles}") # Compute the circle-point and center-point curves (loci of valid # attachment points on the body and on the ground) curves = compute_circle_point_curve(poses) -print(f"{len(curves.circle_curve)} sampled circle points") +print(f"{len(curves.circle_curve)} sampled circle points") # Select compatible dyad pairs to form a complete 4-bar dyads = select_compatible_dyads(curves, max_pairs=20) -print(f"Found {len(dyads)} compatible dyad pairs") +print(f"Found {len(dyads)} compatible dyad pairs") left, right = dyads[0] -print(f"First pair: link lengths {left.link_length:.3f} and {right.link_length:.3f}") +print(f"First pair: link lengths {left.link_length:.3f} and {right.link_length:.3f}") @@ -654,7 +654,7 @@

    Synthesis vs Optimizationverbose=False, ) - print(f"Fine-tuned score: {optimized[0].score:.4f}") + print(f"Fine-tuned score: {optimized[0].score:.4f}") optimized.show(0) diff --git a/docs/tutorials/visualization.html b/docs/tutorials/visualization.html index 0e9b1eb..c31009c 100644 --- a/docs/tutorials/visualization.html +++ b/docs/tutorials/visualization.html @@ -6,14 +6,14 @@ - Visualization Backends — pylinkage 1.2.2 documentation + Visualization Backends — pylinkage 1.3.0 documentation - + @@ -134,18 +134,18 @@

    Visualization Backendsfrom pylinkage.dyads import RRRDyad from pylinkage.simulation import Linkage -A = Ground(0.0, 0.0, name="A") -D = Ground(3.0, 0.0, name="D") -crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank") +A = Ground(0.0, 0.0, name="A") +D = Ground(3.0, 0.0, name="D") +crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank") output = RRRDyad( - anchor1=crank.output, anchor2=D, distance1=3.0, distance2=2.0, name="Output", + anchor1=crank.output, anchor2=D, distance1=3.0, distance2=2.0, name="Output", ) -linkage = Linkage([A, D, crank, output], name="Four-bar") +linkage = Linkage([A, D, crank, output], name="Four-bar") # Every backend accepts precomputed loci; computing them once saves a # simulation per figure loci = list(linkage.step()) -print(f"{len(loci)} frames per turn of the crank") +print(f"{len(loci)} frames per turn of the crank")
    @@ -208,7 +208,7 @@

    Basic Visualizationshow_linkage(linkage) # Longer, with more frames per turn, and a title -show_linkage(linkage, duration=8, fps=30, points=720, title="Four-bar") +show_linkage(linkage, duration=8, fps=30, points=720, title="Four-bar") @@ -226,15 +226,15 @@

    Static Frame Visualizationshow_legend=True, show_labels=True, n_ghosts=6, # outlines at six positions of the cycle - title="Four-bar Linkage - Initial Position", + title="Four-bar Linkage - Initial Position", ) # Customize the plot like any matplotlib axes ax.grid(True, alpha=0.3) -ax.set_aspect("equal") +ax.set_aspect("equal") plt.tight_layout() -plt.savefig("linkage_static.png", dpi=150) +plt.savefig("linkage_static.png", dpi=150) plt.show() @@ -252,9 +252,9 @@

    Animated GIF Outputplot_static_linkage(linkage, ax, loci, show_labels=False) animation = plot_kinematic_linkage(linkage, fig, ax, loci, frames=len(loci), interval=40) -animation.save("four_bar_animation.gif", writer="pillow", fps=24) +animation.save("four_bar_animation.gif", writer="pillow", fps=24) plt.close(fig) -print("Animation saved to four_bar_animation.gif") +print("Animation saved to four_bar_animation.gif")

    Result: An animated GIF showing the linkage cycling through its motion. @@ -265,24 +265,24 @@

    Animated GIF Output

    Compare different configurations side by side:

    def make_fourbar(coupler, rocker, name):
-    A = Ground(0.0, 0.0, name="A")
-    D = Ground(3.0, 0.0, name="D")
+    A = Ground(0.0, 0.0, name="A")
+    D = Ground(3.0, 0.0, name="D")
     crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31)
     output = RRRDyad(
         anchor1=crank.output, anchor2=D, distance1=coupler, distance2=rocker,
     )
     return Linkage([A, D, crank, output], name=name)
 
-linkage1 = make_fourbar(3.0, 2.0, "Short rocker")
-linkage2 = make_fourbar(3.0, 3.0, "Long rocker")
+linkage1 = make_fourbar(3.0, 2.0, "Short rocker")
+linkage2 = make_fourbar(3.0, 3.0, "Long rocker")
 
 fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
 for lk, ax in ((linkage1, ax1), (linkage2, ax2)):
     plot_static_linkage(lk, ax, list(lk.step()), n_ghosts=4, title=lk.name)
-    ax.set_aspect("equal")
+    ax.set_aspect("equal")
 
 plt.tight_layout()
-plt.savefig("comparison.png", dpi=150)
+plt.savefig("comparison.png", dpi=150)
 plt.show()
    @@ -299,7 +299,7 @@

    Basic Interactive Plotfig = plot_linkage_plotly( linkage, loci, - title="Four-bar", + title="Four-bar", show_loci=True, # joint trajectories show_labels=True, # joint names show_dimensions=True, # link lengths @@ -311,7 +311,7 @@

    Basic Interactive Plotfig.show() # Save to HTML -fig.write_html("interactive_linkage.html") +fig.write_html("interactive_linkage.html")

    Result: An interactive HTML page where you can zoom and pan, hover over @@ -325,11 +325,11 @@

    Animation with Sliderfig = animate_linkage_plotly( linkage, loci, - title="Interactive Four-bar", + title="Interactive Four-bar", frame_duration=50, # ms per frame ) -fig.write_html("animated_linkage.html") +fig.write_html("animated_linkage.html")

    Result: HTML with a slider to scrub through the animation manually.

    @@ -340,18 +340,18 @@

    Animation with SliderCustomizing Plotly Appearance

    The returned object is a plain plotly Figure: restyle it with the plotly API.

    -
    fig = plot_linkage_plotly(linkage, loci, title="Styled Four-bar")
+
    fig = plot_linkage_plotly(linkage, loci, title="Styled Four-bar")
 
 # Further customization using the plotly API
 fig.update_layout(
-    plot_bgcolor="white",
-    paper_bgcolor="white",
-    font=dict(family="Arial", size=14),
+    plot_bgcolor="white",
+    paper_bgcolor="white",
+    font=dict(family="Arial", size=14),
 )
-fig.update_xaxes(showgrid=True, gridwidth=1, gridcolor="lightgray")
-fig.update_yaxes(showgrid=True, gridwidth=1, gridcolor="lightgray")
+fig.update_xaxes(showgrid=True, gridwidth=1, gridcolor="lightgray")
+fig.update_yaxes(showgrid=True, gridwidth=1, gridcolor="lightgray")
 # Thicker bars: the link traces are the ones drawn with lines only
-fig.update_traces(line_width=6, selector=dict(mode="lines"))
+fig.update_traces(line_width=6, selector=dict(mode="lines"))
 
 fig.show()
 
    
@@ -362,10 +362,10 @@ 
    Embedding in Web Pages
    fig = plot_linkage_plotly(linkage, loci)
 
 # Get an HTML div for embedding
-div_html = fig.to_html(include_plotlyjs="cdn", full_html=False)
+div_html = fig.to_html(include_plotlyjs="cdn", full_html=False)
 
 # Write to file with custom wrapper
-full_html = f"""
+full_html = f"""
 <!DOCTYPE html>
 <html>
 <head>
@@ -381,9 +381,9 @@ 
    Embedding in Web Pages    <p>Use the controls to explore the mechanism.</p>
 </body>
 </html>
-"""
+"""
 
-with open("embedded_linkage.html", "w") as f:
+with open("embedded_linkage.html", "w") as f:
     f.write(full_html)
 
    
 
    
@@ -397,7 +397,7 @@ 
    Basic SVG Output
    from pylinkage.visualizer import save_linkage_svg
 
 # Save as SVG
-save_linkage_svg(linkage, "linkage.svg", loci)
+save_linkage_svg(linkage, "linkage.svg", loci)

    Result: A crisp SVG file that scales perfectly at any resolution.

    @@ -409,18 +409,18 @@

    Customizing SVG Styledrawing = plot_linkage_svg( linkage, loci, - title="Four-bar", - link_style="bone", # "bar" (default), "bone" or "line" + title="Four-bar", + link_style="bone", # "bar" (default), "bone" or "line" show_dimensions=True, # link lengths along the bars show_loci=True, show_labels=True, scale=60, # pixels per unit padding=80, # canvas margin in pixels ) -print(f"Canvas: {drawing.width} x {drawing.height} px") +print(f"Canvas: {drawing.width} x {drawing.height} px") # The drawsvg Drawing can be edited before saving -drawing.save_svg("styled_linkage.svg") +drawing.save_svg("styled_linkage.svg")

    The same keyword arguments go through save_linkage_svg(linkage, path, @@ -432,7 +432,7 @@

    SVG for LaTeXdrawing.save_png() (needs drawsvg[raster]) or keep the SVG and include it with \includesvg:

    drawing = plot_linkage_svg(linkage, loci, show_labels=True, scale=40, padding=40)
-drawing.save_svg("latex_figure.svg")
+drawing.save_svg("latex_figure.svg")
 
 # Include in LaTeX:
 # \begin{figure}
@@ -461,12 +461,12 @@ 
    DXF Export (2D CAD)
    from pylinkage.visualizer import plot_linkage_dxf, save_linkage_dxf
 
 # Save to DXF file
-save_linkage_dxf(linkage, "linkage.dxf", loci)
+save_linkage_dxf(linkage, "linkage.dxf", loci)
 
 # Or get the ezdxf Drawing object for further customization
 doc = plot_linkage_dxf(linkage, loci)
-print(f"Layers: {[layer.dxf.name for layer in doc.layers]}")
-doc.saveas("custom_linkage.dxf")
+print(f"Layers: {[layer.dxf.name for layer in doc.layers]}")
+doc.saveas("custom_linkage.dxf")

    DXF Layers: The exported DXF contains organized layers:

    @@ -483,7 +483,7 @@

    Customizing DXF Output
    # Export frame 10 of the 20 with custom dimensions
 save_linkage_dxf(
     linkage,
-    "frame10.dxf",
+    "frame10.dxf",
     loci,
     frame_index=10,          # Export this frame (0 = first)
     link_width=0.5,          # Link bar width in world units
@@ -498,11 +498,11 @@ 
    STEP Export (3D CAD)
    from pylinkage.visualizer import build_linkage_3d, save_linkage_step
 
 # Save to STEP file (dimensions auto-scaled to fit linkage)
-save_linkage_step(linkage, "linkage.step", loci)
+save_linkage_step(linkage, "linkage.step", loci)
 
 # Or get the build123d Compound for further manipulation
 model = build_linkage_3d(linkage, loci)
-print(f"{len(list(model.solids()))} solids")
+print(f"{len(list(model.solids()))} solids")

    3D Geometry: The STEP export creates:

    @@ -520,7 +520,7 @@

    Customizing STEP Dimensions# Define custom link cross-section link_profile = LinkProfile( - width=0.3, # Link bar width (in the linkage's units) + width=0.3, # Link bar width (in the linkage's units) thickness=0.1, # Extrusion depth in Z fillet_radius=0.02, # Edge rounding (0 for sharp) ) @@ -534,7 +534,7 @@

    Customizing STEP Dimensions# Export with custom profiles save_linkage_step( linkage, - "machined_linkage.step", + "machined_linkage.step", loci, link_profile=link_profile, joint_profile=joint_profile, @@ -551,11 +551,11 @@

    Exporting Multiple Framesfor i, frame_idx in enumerate([0, 5, 10, 15]): save_linkage_step( linkage, - f"linkage_position_{i}.step", + f"linkage_position_{i}.step", loci, frame_index=frame_idx, ) - print(f"Exported frame {frame_idx} to linkage_position_{i}.step") + print(f"Exported frame {frame_idx} to linkage_position_{i}.step")

    @@ -572,8 +572,8 @@

    CAD Export Workflowshow_linkage, ) -Path("documentation").mkdir(exist_ok=True) -Path("fabrication").mkdir(exist_ok=True) +Path("documentation").mkdir(exist_ok=True) +Path("fabrication").mkdir(exist_ok=True) # 1. Design and simulate loci = list(linkage.step()) @@ -582,21 +582,21 @@

    CAD Export Workflowshow_linkage(linkage, loci=loci) # 3. Publication figure (SVG) -save_linkage_svg(linkage, "documentation/linkage.svg", loci, show_loci=True) +save_linkage_svg(linkage, "documentation/linkage.svg", loci, show_loci=True) # 4. 2D CAD for laser cutting (DXF) -save_linkage_dxf(linkage, "fabrication/linkage_2d.dxf", loci) +save_linkage_dxf(linkage, "fabrication/linkage_2d.dxf", loci) # 5. 3D CAD for machining/printing (STEP) profile = LinkProfile(width=0.3, thickness=0.1) save_linkage_step( linkage, - "fabrication/linkage_3d.step", + "fabrication/linkage_3d.step", loci, link_profile=profile, ) -print("Export complete! Files ready for fabrication.") +print("Export complete! Files ready for fabrication.") @@ -617,7 +617,7 @@

    PSO Visualization@pl.kinematic_maximization def stride(loci, **kwargs): - """Horizontal travel of the output joint.""" + """Horizontal travel of the output joint.""" xs = [step[-1][0] for step in loci] return max(xs) - min(xs) @@ -643,22 +643,22 @@

    PSO Visualization(i, history[i * n_particles:(i + 1) * n_particles]) for i in range(len(history) // n_particles) ] -dim_names = ["crank radius", "coupler", "rocker"] -dim_types = ["length", "length", "length"] +dim_names = ["crank radius", "coupler", "rocker"] +dim_types = ["length", "length", "length"] # Parallel coordinates of the final swarm, colored by score fig, ax = plt.subplots(figsize=(10, 5)) parallel_coordinates_plot(swarms[-1], dim_names, dim_types, bounds=bounds, ax=ax) -fig.savefig("pso_parallel_coordinates.png", dpi=150) +fig.savefig("pso_parallel_coordinates.png", dpi=150) # Dashboard: score history, the swarm, and the best linkage score_history = [max(agent[0] for agent in swarm) for _, swarm in swarms] fig = dashboard_layout(linkage, swarms[-1], score_history, dim_names, dim_types, bounds=bounds) -fig.savefig("pso_dashboard.png", dpi=150) +fig.savefig("pso_dashboard.png", dpi=150) # Animated dashboard over the iterations animation = animate_dashboard(linkage, swarms, dim_names, dim_types, bounds=bounds, interval=300) -animation.save("pso_dashboard.gif", writer="pillow", fps=3) +animation.save("pso_dashboard.gif", writer="pillow", fps=3)

    The strider example (docs/examples/pso_visualization_demo.py) runs the @@ -677,7 +677,7 @@

    Visualization with Kinematics
    from pylinkage.visualizer import animate_kinematics, show_kinematics
 
-# Set the crank's physical angular velocity (rad/s)
+# Set the crank's physical angular velocity (rad/s)
 linkage.set_input_velocity(crank, omega=10.0)
 
 # Show single frame with velocity vectors
@@ -688,14 +688,14 @@ 
    Visualization with Kinematicsshow_acceleration=True,
     velocity_scale=0.05,       # Scale factor for arrow length
 )
-fig.savefig("velocities.png")
+fig.savefig("velocities.png")
 
 # Animated with velocities
 animate_kinematics(
     linkage,
     show_velocity=True,
     duration=2.0,
-    save_path="velocity_animation.gif",
+    save_path="velocity_animation.gif",
 )
    @@ -753,14 +753,14 @@

    Example: Complete Visualization Workflow) # Create an optimized linkage -A = Ground(0.0, 0.0, name="A") -D = Ground(3.0, 0.0, name="D") -crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank") +A = Ground(0.0, 0.0, name="A") +D = Ground(3.0, 0.0, name="D") +crank = Crank(anchor=A, radius=1.0, angular_velocity=0.31, name="Crank") output = RRRDyad( anchor1=crank.output, anchor2=D, - distance1=2.5, distance2=1.5, name="Output", + distance1=2.5, distance2=1.5, name="Output", ) -linkage = Linkage([A, D, crank, output], name="Optimized Four-bar") +linkage = Linkage([A, D, crank, output], name="Optimized Four-bar") loci = list(linkage.step()) # 1. Quick check with Matplotlib @@ -768,27 +768,27 @@

    Example: Complete Visualization Workflow# 2. Interactive exploration with Plotly fig = animate_linkage_plotly(linkage, loci) -fig.write_html("explore.html") -print("Open explore.html in browser for interactive view") +fig.write_html("explore.html") +print("Open explore.html in browser for interactive view") # 3. Publication figure with drawsvg save_linkage_svg( linkage, - "figure1.svg", + "figure1.svg", loci, show_loci=True, show_labels=True, - link_style="line", + link_style="line", ) -print("Publication figure saved to figure1.svg") +print("Publication figure saved to figure1.svg") # 4. Animation for presentation fig, ax = plt.subplots(figsize=(6, 4.5)) plot_static_linkage(linkage, ax, loci, show_labels=False) animation = plot_kinematic_linkage(linkage, fig, ax, loci, frames=len(loci)) -animation.save("presentation.gif", writer="pillow", fps=30) +animation.save("presentation.gif", writer="pillow", fps=30) plt.close(fig) -print("Animation saved to presentation.gif") +print("Animation saved to presentation.gif") diff --git a/pyproject.toml b/pyproject.toml index bd63f05..d79f1d7 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -4,7 +4,7 @@ build-backend = "hatchling.build" [project] name = "pylinkage" -version = "1.2.2" +version = "1.3.0" authors = [ {name = "Hugo Farajallah", email = "contact@hugofara.net"}, ] @@ -155,7 +155,7 @@ format = "ruff format ." typecheck = "mypy src/pylinkage" [tool.bumpversion] -current_version = "1.2.2" +current_version = "1.3.0" commit = true tag = true tag_name = "v{new_version}" diff --git a/src/pylinkage/__init__.py b/src/pylinkage/__init__.py index d139ead..113e90b 100644 --- a/src/pylinkage/__init__.py +++ b/src/pylinkage/__init__.py @@ -244,4 +244,4 @@ def __getattr__(name: str) -> object: raise AttributeError(f"module {__name__!r} has no attribute {name!r}") -__version__ = "1.2.2" +__version__ = "1.3.0" diff --git a/uv.lock b/uv.lock index acbeea4..a9abe74 100644 --- a/uv.lock +++ b/uv.lock @@ -3179,7 +3179,7 @@ wheels = [ [[package]] name = "pylinkage" -version = "1.2.2" +version = "1.3.0" source = { editable = "." } dependencies = [ { name = "numpy", version = "2.4.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.12'" },