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RevolutePlanarLoopConstraint.md

RevolutePlanarLoopConstraint ​

Revolute joint for closing planar kinematic loops.

When a closed loop of parallel-axis revolute joints exists (e.g. a 4-bar linkage), one of the joints must be replaced with this variant to break the mathematical redundancy of the cut-forces perpendicular to the loop plane. This joint enforces only the two in-plane position constraints between frame_a and frame_b; the orientation is left free (determined by the rest of the loop) and torques as well as the axis-aligned cut force are set to zero.

  • n: rotation axis (unit vector), resolved in frame_a

This component extends from PartialTwoFrames This component extends from Renderable

Usage ​

MultibodyComponents.RevolutePlanarLoopConstraint(render=true, color=world_default_joint_color(), specular_coefficient=1.5, n=[0, 0, 1], radius=world_default_joint_width() / 2, cylinder_length=world_default_joint_length(), e=n / norm_(n), nnx_a=ifelse(abs(n[1]) > 0.1, [0, 1, 0], ifelse(abs(n[2]) > 0.1, [0, 0, 1], [1, 0, 0])), ey_a=cross(n, nnx_a) / norm_(cross(n, nnx_a)), ex_a=cross(ey_a, n))

Parameters: ​

NameDescriptionUnitsDefault value
render–true
color–world_defau...int_color()
specular_coefficient–1.5
naxis of rotation (unit vector) resolved in frame_a–[0, 0, 1]
radiusRadius of the revolute cylinder in animations–world_defau...width() / 2
cylinder_lengthLength of the revolute cylinder in animations–world_defau...nt_length()

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)

Variables ​

NameDescriptionUnits
r_rel_aPosition vector from origin of frame_a to origin of frame_b, resolved in frame_am
f_cConstraint forces along (ex_a, ey_a)–
R_relRelative rotation matrix from frame_a to frame_b coordinates–

Behavior ​

Dict{MIME{Symbol("text/plain")}, String} with 1 entry: MIME type text/plain => "Error displaying result"

Source ​

dyad
"""
Revolute joint for closing planar kinematic loops.

When a closed loop of parallel-axis revolute joints exists (e.g. a 4-bar
linkage), one of the joints must be replaced with this variant to break the
mathematical redundancy of the cut-forces perpendicular to the loop plane.
This joint enforces only the two in-plane position constraints between
`frame_a` and `frame_b`; the orientation is left free (determined by the
rest of the loop) and torques as well as the axis-aligned cut force are
set to zero.

- `n`: rotation axis (unit vector), resolved in frame_a
"""
component RevolutePlanarLoopConstraint
  extends PartialTwoFrames()
  extends Renderable(color = world_default_joint_color())
  shape = CylinderShape(render = render, color = color, r = frame_a.r_0, R = transpose(frame_a.R), r_shape = n * (-cylinder_length / 2), length_direction = n, length = cylinder_length, width = 2 * radius, height = 2 * radius)
  "axis of rotation (unit vector) resolved in frame_a"
  parameter n::Real[3] = [0, 0, 1]
  "Radius of the revolute cylinder in animations"
  parameter radius::Real = world_default_joint_width() / 2
  "Length of the revolute cylinder in animations"
  parameter cylinder_length::Real = world_default_joint_length()
  final parameter e::Real[3] = n / norm_(n)
  final parameter nnx_a::Real[3] = ifelse(abs(n[1]) > 0.1, [0, 1, 0], ifelse(abs(n[2]) > 0.1, [0, 0, 1], [1, 0, 0])) # WORKAROUND: ones(Bool, 3) in condition should not be required
  final parameter ey_a::Real[3] = cross(n, nnx_a) / norm_(cross(n, nnx_a))
  final parameter ex_a::Real[3] = cross(ey_a, n)
  "Position vector from origin of frame_a to origin of frame_b, resolved in frame_a"
  variable r_rel_a::Position[3]
  "Constraint forces along (ex_a, ey_a)"
  variable f_c::Real[2]
  "Relative rotation matrix from frame_a to frame_b coordinates"
  variable R_rel::Real[3, 3]
relations
  R_rel = frame_b.R * transpose(frame_a.R)
  r_rel_a = resolve2(frame_a.R, frame_b.r_0 - frame_a.r_0)
  0 = dot(ex_a, r_rel_a)
  0 = dot(ey_a, r_rel_a)
  frame_a.tau = [0, 0, 0]
  frame_b.tau = [0, 0, 0]
  frame_a.f = ex_a * f_c[1] + ey_a * f_c[2]
  frame_b.f = -R_rel * frame_a.f
  assert(abs(dot(e, r_rel_a)) <= 1e-10 and abs(dot(e, resolve2(R_rel, ex_a))) <= 1e-10 and abs(dot(e, resolve2(R_rel, ey_a))) <= 1e-10, "The RevolutePlanarLoopConstraint joint is used as cut-joint of a planar loop. However, the revolute joint is not part of a planar loop where the axis of the revolute joint (parameter n) is orthogonal to the possible movements. Either use instead joint Revolute or correct the definition of the axis vector n in the revolute joints of the planar loop.")
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/RevolutePlanarLoopConstraint.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 200,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end
Flattened Source
dyad
"""
Revolute joint for closing planar kinematic loops.

When a closed loop of parallel-axis revolute joints exists (e.g. a 4-bar
linkage), one of the joints must be replaced with this variant to break the
mathematical redundancy of the cut-forces perpendicular to the loop plane.
This joint enforces only the two in-plane position constraints between
`frame_a` and `frame_b`; the orientation is left free (determined by the
rest of the loop) and torques as well as the axis-aligned cut force are
set to zero.

- `n`: rotation axis (unit vector), resolved in frame_a
"""
component RevolutePlanarLoopConstraint
  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
  shape = CylinderShape(render = render, color = color, r = frame_a.r_0, R = transpose(frame_a.R), r_shape = n * (-cylinder_length / 2), length_direction = n, length = cylinder_length, width = 2 * radius, height = 2 * radius)
  "axis of rotation (unit vector) resolved in frame_a"
  parameter n::Real[3] = [0, 0, 1]
  "Radius of the revolute cylinder in animations"
  parameter radius::Real = world_default_joint_width() / 2
  "Length of the revolute cylinder in animations"
  parameter cylinder_length::Real = world_default_joint_length()
  final parameter e::Real[3] = n / norm_(n)
  final parameter nnx_a::Real[3] = ifelse(abs(n[1]) > 0.1, [0, 1, 0], ifelse(abs(n[2]) > 0.1, [0, 0, 1], [1, 0, 0])) # WORKAROUND: ones(Bool, 3) in condition should not be required
  final parameter ey_a::Real[3] = cross(n, nnx_a) / norm_(cross(n, nnx_a))
  final parameter ex_a::Real[3] = cross(ey_a, n)
  "Position vector from origin of frame_a to origin of frame_b, resolved in frame_a"
  variable r_rel_a::Position[3]
  "Constraint forces along (ex_a, ey_a)"
  variable f_c::Real[2]
  "Relative rotation matrix from frame_a to frame_b coordinates"
  variable R_rel::Real[3, 3]
relations
  R_rel = frame_b.R * transpose(frame_a.R)
  r_rel_a = resolve2(frame_a.R, frame_b.r_0 - frame_a.r_0)
  0 = dot(ex_a, r_rel_a)
  0 = dot(ey_a, r_rel_a)
  frame_a.tau = [0, 0, 0]
  frame_b.tau = [0, 0, 0]
  frame_a.f = ex_a * f_c[1] + ey_a * f_c[2]
  frame_b.f = -R_rel * frame_a.f
  assert(abs(dot(e, r_rel_a)) <= 1e-10 and abs(dot(e, resolve2(R_rel, ex_a))) <= 1e-10 and abs(dot(e, resolve2(R_rel, ey_a))) <= 1e-10, "The RevolutePlanarLoopConstraint joint is used as cut-joint of a planar loop. However, the revolute joint is not part of a planar loop where the axis of the revolute joint (parameter n) is orthogonal to the possible movements. Either use instead joint Revolute or correct the definition of the axis vector n in the revolute joints of the planar loop.")
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/RevolutePlanarLoopConstraint.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 200,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end


Test Cases ​

No test cases defined.

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