LIBRARY

JointSSP

Spherical - spherical - prismatic joint aggregation. Analytically closes a kinematic loop (no constraints, no potential states): a SphericalSpherical rod of fixed length rod1_length (optionally carrying a point mass rod1_mass) between frame_a and the middle spherical joint, a rigid rod rRod2_ib, and a PrismaticWithLengthConstraint at frame_b. Interior frames frame_ib and frame_im (rod2 ends) are exposed. axis/bearing drive the prismatic joint.

This component extends from PartialTwoFrames

Usage

MultibodyComponents.JointSSP(rod1_length=1, rod1_mass=0, n_b=[0, 0, 1], rRod2_ib=[1, 0, 0], s_offset=0, s_guess=0, rod_radius=0.05, rod_color=[0.5, 0, 0.5, 1])

Parameters:

Name	Description	Units	Default value
positive_branch		–	true
has_mass		–	false
rod1_length	Distance between the origins of the two spherical joints (rod1 length)	–	1
rod1_mass	Mass of rod1 (point mass located in the middle of rod1)	kg	0
n_b	Axis of the prismatic joint, resolved in frame_b	–	[0, 0, 1]
rRod2_ib	Vector from frame_ib origin to the middle spherical joint, resolved in frame_ib	–	[1, 0, 0]
s_offset	Relative distance offset of the prismatic joint	–	0
s_guess	Guess value for the prismatic distance at the initial time	–	0
rod_radius	Rendering radius of the rods	–	0.05
rod_color	RGBA color of the rods	–	[0.5, 0, 0.5, 1]

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)

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

connectors that can be connected together (Frame3D)

• axis - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

• bearing - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

Variables

Name	Description	Units
aux	Denominator used to compute the rod force	–
f_rod	Constraint force in the direction of rod1 (positive if the rod is pressed)	–

Behavior

Source

"""
Spherical - spherical - prismatic joint aggregation. Analytically closes a
kinematic loop (no constraints, no potential states): a `SphericalSpherical` rod
of fixed length `rod1_length` (optionally carrying a point mass `rod1_mass`)
between `frame_a` and the middle spherical joint, a rigid rod `rRod2_ib`, and a
`PrismaticWithLengthConstraint` at `frame_b`. Interior frames `frame_ib` and
`frame_im` (rod2 ends) are exposed. `axis`/`bearing` drive the prismatic joint.
"""
component JointSSP
  extends PartialTwoFrames()
  "Frame fixed in rod2 at the prismatic side (= rod2.frame_a)"
  frame_ib = Frame3D() {}
  "Frame fixed in rod2 at the middle spherical joint (= rod2.frame_b)"
  frame_im = Frame3D() {}
  "Translational flange driving the prismatic joint"
  axis = Flange() {}
  "Translational flange of the prismatic joint bearing"
  bearing = Flange() {}
  rod1 = SphericalSpherical(r_0 = [rod1_length, 0, 0], kinematic_constraint = false, constraint_residue_external = true, has_mass = has_mass, m = rod1_mass, radius = rod_radius, color = rod_color) {}
  rod2 = FixedTranslation(r = rRod2_ib, radius = rod_radius, color = rod_color) {}
  prismatic = PrismaticWithLengthConstraint(n = n_b, length_constraint = rod1_length, s_offset = s_offset, s_guess = s_guess, positive_branch = positive_branch) {}
  structural parameter positive_branch::Boolean = true
  structural parameter has_mass::Boolean = false
  "Distance between the origins of the two spherical joints (rod1 length)"
  parameter rod1_length::Real = 1
  "Mass of rod1 (point mass located in the middle of rod1)"
  parameter rod1_mass::Mass = 0 if has_mass
  "Axis of the prismatic joint, resolved in frame_b"
  parameter n_b::Real[3] = [0, 0, 1]
  "Vector from frame_ib origin to the middle spherical joint, resolved in frame_ib"
  parameter rRod2_ib::Real[3] = [1, 0, 0]
  "Relative distance offset of the prismatic joint"
  parameter s_offset::Real = 0
  "Guess value for the prismatic distance at the initial time"
  parameter s_guess::Real = 0
  "Rendering radius of the rods"
  parameter rod_radius::Real = 0.05
  "RGBA color of the rods"
  parameter rod_color::Real[4] = [0.5, 0, 0.5, 1]
  "Denominator used to compute the rod force"
  variable aux::Real
  "Constraint force in the direction of rod1 (positive if the rod is pressed)"
  variable f_rod::Real
relations
  aux = dot(prismatic.e, resolve_relative(rod1.eRod_a, rod1.frame_a.R, rod1.frame_b.R))
  f_rod = (-prismatic.f - dot(prismatic.e, frame_ib.f + frame_im.f)) / ifelse(abs(aux) < 1e-10, 1e-10, aux)
  rod1.constraint_residue = rod1.f_rod - f_rod
  prismatic.r_a = resolve2(frame_b.R, frame_a.r_0 - frame_b.r_0)
  prismatic.r_b = rRod2_ib
  connect(prismatic.frame_b, rod2.frame_a)
  connect(rod2.frame_b, rod1.frame_b)
  connect(prismatic.frame_a, frame_b)
  connect(rod2.frame_a, frame_ib)
  connect(rod1.frame_a, frame_a)
  connect(rod2.frame_b, frame_im)
  connect(prismatic.axis, axis)
  connect(prismatic.bearing, bearing)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/JointSSP.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 200,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end

Flattened Source

"""
Spherical - spherical - prismatic joint aggregation. Analytically closes a
kinematic loop (no constraints, no potential states): a `SphericalSpherical` rod
of fixed length `rod1_length` (optionally carrying a point mass `rod1_mass`)
between `frame_a` and the middle spherical joint, a rigid rod `rRod2_ib`, and a
`PrismaticWithLengthConstraint` at `frame_b`. Interior frames `frame_ib` and
`frame_im` (rod2 ends) are exposed. `axis`/`bearing` drive the prismatic joint.
"""
component JointSSP
  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": []
    }
  }
  "Frame fixed in rod2 at the prismatic side (= rod2.frame_a)"
  frame_ib = Frame3D() {}
  "Frame fixed in rod2 at the middle spherical joint (= rod2.frame_b)"
  frame_im = Frame3D() {}
  "Translational flange driving the prismatic joint"
  axis = Flange() {}
  "Translational flange of the prismatic joint bearing"
  bearing = Flange() {}
  rod1 = SphericalSpherical(r_0 = [rod1_length, 0, 0], kinematic_constraint = false, constraint_residue_external = true, has_mass = has_mass, m = rod1_mass, radius = rod_radius, color = rod_color) {}
  rod2 = FixedTranslation(r = rRod2_ib, radius = rod_radius, color = rod_color) {}
  prismatic = PrismaticWithLengthConstraint(n = n_b, length_constraint = rod1_length, s_offset = s_offset, s_guess = s_guess, positive_branch = positive_branch) {}
  structural parameter positive_branch::Boolean = true
  structural parameter has_mass::Boolean = false
  "Distance between the origins of the two spherical joints (rod1 length)"
  parameter rod1_length::Real = 1
  "Mass of rod1 (point mass located in the middle of rod1)"
  parameter rod1_mass::Mass = 0 if has_mass
  "Axis of the prismatic joint, resolved in frame_b"
  parameter n_b::Real[3] = [0, 0, 1]
  "Vector from frame_ib origin to the middle spherical joint, resolved in frame_ib"
  parameter rRod2_ib::Real[3] = [1, 0, 0]
  "Relative distance offset of the prismatic joint"
  parameter s_offset::Real = 0
  "Guess value for the prismatic distance at the initial time"
  parameter s_guess::Real = 0
  "Rendering radius of the rods"
  parameter rod_radius::Real = 0.05
  "RGBA color of the rods"
  parameter rod_color::Real[4] = [0.5, 0, 0.5, 1]
  "Denominator used to compute the rod force"
  variable aux::Real
  "Constraint force in the direction of rod1 (positive if the rod is pressed)"
  variable f_rod::Real
relations
  aux = dot(prismatic.e, resolve_relative(rod1.eRod_a, rod1.frame_a.R, rod1.frame_b.R))
  f_rod = (-prismatic.f - dot(prismatic.e, frame_ib.f + frame_im.f)) / ifelse(abs(aux) < 1e-10, 1e-10, aux)
  rod1.constraint_residue = rod1.f_rod - f_rod
  prismatic.r_a = resolve2(frame_b.R, frame_a.r_0 - frame_b.r_0)
  prismatic.r_b = rRod2_ib
  connect(prismatic.frame_b, rod2.frame_a)
  connect(rod2.frame_b, rod1.frame_b)
  connect(prismatic.frame_a, frame_b)
  connect(rod2.frame_a, frame_ib)
  connect(rod1.frame_a, frame_a)
  connect(rod2.frame_b, frame_im)
  connect(prismatic.axis, axis)
  connect(prismatic.bearing, bearing)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/JointSSP.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 200,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

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