LIBRARY

SpringDamperParallel

Linear spring and linear damper in parallel acting as line force between frame_a and frame_b.

f = c * (s - s_unstretched) + d * D(s)

This component extends from PartialLineForce This component extends from Renderable

Usage

MultibodyComponents.SpringDamperParallel(s_small=1e-10, render=true, color=world_default_spring_color(), specular_coefficient=1.5, c=1.0, d=1.0, s_unstretched=0, radius=world_default_force_width(), num_windings=6, N=200, end_ratio=0.1)

Parameters:

Name	Description	Units	Default value
fixed_rotation_at_frame_a		–	false
fixed_rotation_at_frame_b		–	false
s_small		–	1e-10
render		–	true
color		–	world_defau...ing_color()
specular_coefficient		–	1.5
c	Spring constant	N/m	1.0
d	Damping coefficient	N.s/m	1.0
s_unstretched	Unstretched spring length	m	0
radius	Radius in animations	–	world_defau...rce_width()
num_windings	Number of windings in animations	–	6
N	Number of points used to render each winding	–	200
end_ratio	Fraction of total length used for the tapered ends	–	0.1

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)

Variables

Name	Description	Units
length	Distance between the origin of frame_a and the origin of frame_b	m
s	(Guarded) distance between the origin of frame_a and the origin of frame_b (>= s_small))	m
r_rel_0	Position vector from frame_a to frame_b resolved in world frame	m
e_rel_0	Unit vector in direction from frame_a to frame_b, resolved in world frame	–
r_rel_a	Position vector from frame_a to frame_b, resolved in frame_a	m
e_a	Unit vector from frame_a to frame_b, resolved in frame_a	–
f	Scalar line force (positive = tension)	N

Behavior

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

Source

"""
Linear spring and linear damper in parallel acting as line force between
`frame_a` and `frame_b`.

`f = c * (s - s_unstretched) + d * D(s)`
"""
component SpringDamperParallel
  extends PartialLineForce
  extends Renderable(color = world_default_spring_color())
  # Visualization shape
  spring_shape = SpringShape(render = render, color = color, num_windings = num_windings, N = N, end_ratio = end_ratio, r = frame_a.r_0, length_direction = r_rel_0, length = s, width = radius)
  "Spring constant"
  parameter c::TranslationalSpringConstant = 1.0
  "Damping coefficient"
  parameter d::TranslationalDampingConstant = 1.0
  "Unstretched spring length"
  parameter s_unstretched::Length = 0
  "Radius in animations"
  parameter radius::Real = world_default_force_width()
  "Number of windings in animations"
  parameter num_windings::Real = 6
  "Number of points used to render each winding"
  parameter N::Integer = 200
  "Fraction of total length used for the tapered ends"
  parameter end_ratio::Real = 0.1
relations
  f = c * (s - s_unstretched) + d * der(s)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/SpringDamper.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 100,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end

Flattened Source

"""
Linear spring and linear damper in parallel acting as line force between
`frame_a` and `frame_b`.

`f = c * (s - s_unstretched) + d * D(s)`
"""
component SpringDamperParallel
  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": []
    }
  }
  structural parameter fixed_rotation_at_frame_a::Boolean = false
  structural parameter fixed_rotation_at_frame_b::Boolean = false
  parameter s_small::Real = 1e-10
  "Distance between the origin of frame_a and the origin of frame_b"
  variable length::Length
  "(Guarded) distance between the origin of frame_a and the origin of frame_b (>= s_small))"
  variable s::Length
  "Position vector from frame_a to frame_b resolved in world frame"
  variable r_rel_0::Position[3]
  "Unit vector in direction from frame_a to frame_b, resolved in world frame"
  variable e_rel_0::Real[3]
  "Position vector from frame_a to frame_b, resolved in frame_a"
  variable r_rel_a::Position[3]
  "Unit vector from frame_a to frame_b, resolved in frame_a"
  variable e_a::Real[3]
  "Scalar line force (positive = tension)"
  variable f::Dyad.Force
  parameter render::Boolean = true
  parameter color::Real[4] = [0.5, 0.5, 0.5, 1.0]
  parameter specular_coefficient::Real = 1.5
  # Visualization shape
  spring_shape = SpringShape(render = render, color = color, num_windings = num_windings, N = N, end_ratio = end_ratio, r = frame_a.r_0, length_direction = r_rel_0, length = s, width = radius)
  "Spring constant"
  parameter c::TranslationalSpringConstant = 1.0
  "Damping coefficient"
  parameter d::TranslationalDampingConstant = 1.0
  "Unstretched spring length"
  parameter s_unstretched::Length = 0
  "Radius in animations"
  parameter radius::Real = world_default_force_width()
  "Number of windings in animations"
  parameter num_windings::Real = 6
  "Number of points used to render each winding"
  parameter N::Integer = 200
  "Fraction of total length used for the tapered ends"
  parameter end_ratio::Real = 0.1
relations
  # Relative position and distance
  r_rel_0 = frame_b.r_0 - frame_a.r_0
  length = norm_(r_rel_0)
  assert(length > s_small, "The distance between the origin of frame_a and the origin of frame_b of a line force component became smaller than parameter s_small.")
  s = max(length, s_small)
  e_rel_0 = r_rel_0 / s
  # frame_a: fix rotation to identity or set tau = 0
  if fixed_rotation_at_frame_a
    frame_a.R = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
  else
    frame_a.tau = [0, 0, 0]
  end
  # frame_b: fix rotation to identity or set tau = 0
  if fixed_rotation_at_frame_b
    frame_b.R = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
  else
    frame_b.tau = [0, 0, 0]
  end
  r_rel_a = resolve2(frame_a.R, r_rel_0)
  e_a = r_rel_a / s
  frame_a.f = -e_a * f
  frame_b.f = -resolve2(frame_b.R, resolve1(frame_a.R, frame_a.f))
  f = c * (s - s_unstretched) + d * der(s)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/SpringDamper.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 100,
        "rot": 0,
        "attrs": {"font-size": "160"}
      }
    ]
  }
}
end

Test Cases

No test cases defined.

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