LIBRARY

Cable

Cable / rope of total length l and mass m, modeled as n rigid BodyShape segments connected by 3-DOF Spherical joints, matching the Multibody.jl Rope.

When end_joints = true (default), the topology uses n + 1 joints: frame_a → S₁ → link₁ → S₂ → … → Sₙ → linkₙ → Sₙ₊₁ → frame_b

When end_joints = false, only the n − 1 internal joints are kept and both ends attach rigidly to the adjacent frame: frame_a → link₁ → S₁ → link₂ → … → Sₙ₋₁ → linkₙ → frame_b

Each Spherical joint uses quaternion state (Euler-angle state hits a structural-simplify cycle when chained — SciML/ModelingToolkit.jl#4608) and transmits no torque. The cable starts straight (along dir); seed an initial bend by setting a joint's non-unit quaternion Q_hat as an initial condition, e.g. a 0.9 rad bend about x on the first joint: cable.joints[1].Q_hat = [cos(0.45), sin(0.45), 0, 0].

This component extends from PartialTwoFrames This component extends from Renderable

Usage

MultibodyComponents.Cable(render=true, color=[0.5, 0.4, 0.4, 1], specular_coefficient=1.5, l=1, m=1, dir=[0, -1, 0], radius=0.05, r_segment=(l / n) * (dir / norm_(dir)), m_segment=m / n)

Parameters:

Name	Description	Units	Default value
orientation_state		–	Orientation...uaternion()
n	Number of rigid segments	–	5
end_joints	Include Spherical joints at both ends (frame_a and frame_b)	–	true
nj	Number of joints	–	ifelse(end_...+ 1, n - 1)
render		–	true
color		–	[0.5, 0.4, 0.4, 1]
specular_coefficient		–	1.5
l	Total unstretched length of the rope	m	1
m	Total mass of the rope (each segment gets m/n)	kg	1
dir	Hanging direction; unit-normalized internally	–	[0, -1, 0]
radius	Rendering radius of each segment	–	0.05

Connectors

• frame_a - Frame3D is the fundamental 3D connector used for 6DOF motion. Most components have one or several Frame

connectors that can be connected together (Frame3D)

• frame_b - Frame3D is the fundamental 3D connector used for 6DOF motion. Most components have one or several Frame

connectors that can be connected together (Frame3D)

Behavior

Source

"""
Cable / rope of total length `l` and mass `m`, modeled as `n` rigid
`BodyShape` segments connected by 3-DOF `Spherical` joints, matching the
Multibody.jl `Rope`.

When `end_joints = true` (default), the topology uses `n + 1` joints:
`frame_a → S₁ → link₁ → S₂ → … → Sₙ → linkₙ → Sₙ₊₁ → frame_b`

When `end_joints = false`, only the `n − 1` internal joints are kept and
both ends attach rigidly to the adjacent frame:
`frame_a → link₁ → S₁ → link₂ → … → Sₙ₋₁ → linkₙ → frame_b`

Each `Spherical` joint uses quaternion state (Euler-angle state hits a
structural-simplify cycle when chained — SciML/ModelingToolkit.jl#4608) and
transmits no torque. The cable starts straight (along `dir`); seed an initial
bend by setting a joint's non-unit quaternion `Q_hat` as an initial condition,
e.g. a 0.9 rad bend about x on the first joint:
`cable.joints[1].Q_hat = [cos(0.45), sin(0.45), 0, 0]`.
"""
component Cable
  extends PartialTwoFrames()
  extends Renderable(color = [0.5, 0.4, 0.4, 1])
  joints = [MultibodyComponents.Spherical(orientation_state = orientation_state, render = false) for i in 1:nj]
  links = [MultibodyComponents.BodyShape(r = r_segment, m = m_segment, color = color, radius = radius) for i in 1:n]
  structural parameter orientation_state::MultibodyComponents.OrientationState = OrientationState.Quaternion()
  "Number of rigid segments"
  structural parameter n::Integer = 5
  "Include Spherical joints at both ends (frame_a and frame_b)"
  structural parameter end_joints::Boolean = true
  "Number of joints"
  final structural parameter nj::Integer = ifelse(end_joints, n + 1, n - 1)
  "Total unstretched length of the rope"
  parameter l::Length = 1
  "Total mass of the rope (each segment gets m/n)"
  parameter m::Mass = 1
  "Hanging direction; unit-normalized internally"
  parameter dir::Real[3] = [0, -1, 0]
  "Rendering radius of each segment"
  parameter radius::Real = 0.05
  final parameter r_segment::Length[3] = (l / n) * (dir / norm_(dir))
  final parameter m_segment::Mass = m / n
relations
  if end_joints
    connect(frame_a, joints[1].frame_a)
    for i in 1:n
      connect(joints[i].frame_b, links[i].frame_a)
      connect(links[i].frame_b, joints[i + 1].frame_a)
    end
    connect(joints[nj].frame_b, frame_b)
  else
    connect(frame_a, links[1].frame_a)
    for i in 1:nj
      connect(links[i].frame_b, joints[i].frame_a)
      connect(joints[i].frame_b, links[i + 1].frame_a)
    end
    connect(links[n].frame_b, frame_b)
  end
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/Cable.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 150,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end

Flattened Source

"""
Cable / rope of total length `l` and mass `m`, modeled as `n` rigid
`BodyShape` segments connected by 3-DOF `Spherical` joints, matching the
Multibody.jl `Rope`.

When `end_joints = true` (default), the topology uses `n + 1` joints:
`frame_a → S₁ → link₁ → S₂ → … → Sₙ → linkₙ → Sₙ₊₁ → frame_b`

When `end_joints = false`, only the `n − 1` internal joints are kept and
both ends attach rigidly to the adjacent frame:
`frame_a → link₁ → S₁ → link₂ → … → Sₙ₋₁ → linkₙ → frame_b`

Each `Spherical` joint uses quaternion state (Euler-angle state hits a
structural-simplify cycle when chained — SciML/ModelingToolkit.jl#4608) and
transmits no torque. The cable starts straight (along `dir`); seed an initial
bend by setting a joint's non-unit quaternion `Q_hat` as an initial condition,
e.g. a 0.9 rad bend about x on the first joint:
`cable.joints[1].Q_hat = [cos(0.45), sin(0.45), 0, 0]`.
"""
component Cable
  frame_a = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -50, "y1": 450, "x2": 50, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  frame_b = Frame3D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 950, "y1": 450, "x2": 1050, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  parameter render::Boolean = true
  parameter color::Real[4] = [0.5, 0.5, 0.5, 1.0]
  parameter specular_coefficient::Real = 1.5
  joints = [MultibodyComponents.Spherical(orientation_state = orientation_state, render = false) for i in 1:nj]
  links = [MultibodyComponents.BodyShape(r = r_segment, m = m_segment, color = color, radius = radius) for i in 1:n]
  structural parameter orientation_state::MultibodyComponents.OrientationState = OrientationState.Quaternion()
  "Number of rigid segments"
  structural parameter n::Integer = 5
  "Include Spherical joints at both ends (frame_a and frame_b)"
  structural parameter end_joints::Boolean = true
  "Number of joints"
  final structural parameter nj::Integer = ifelse(end_joints, n + 1, n - 1)
  "Total unstretched length of the rope"
  parameter l::Length = 1
  "Total mass of the rope (each segment gets m/n)"
  parameter m::Mass = 1
  "Hanging direction; unit-normalized internally"
  parameter dir::Real[3] = [0, -1, 0]
  "Rendering radius of each segment"
  parameter radius::Real = 0.05
  final parameter r_segment::Length[3] = (l / n) * (dir / norm_(dir))
  final parameter m_segment::Mass = m / n
relations
  if end_joints
    connect(frame_a, joints[1].frame_a)
    for i in 1:n
      connect(joints[i].frame_b, links[i].frame_a)
      connect(links[i].frame_b, joints[i + 1].frame_a)
    end
    connect(joints[nj].frame_b, frame_b)
  else
    connect(frame_a, links[1].frame_a)
    for i in 1:nj
      connect(links[i].frame_b, joints[i].frame_a)
      connect(joints[i].frame_b, links[i + 1].frame_a)
    end
    connect(links[n].frame_b, frame_b)
  end
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/Cable.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 150,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • TestCableEndJoints

  • TestCableNoEndJoints

  • TestPlanarCableEndJoints

  • TestPlanarCableNoEndJoints