LIBRARY

PlanarMechanics.Prismatic

Prismatic (sliding) joint allowing translation along a fixed direction.

The sliding direction is given by parameter r, rotated by frame_a's orientation. Without axisflange support, the joint slides freely (f = 0).

This component extends from PartialTwoFrames This component extends from MultibodyComponents.Renderable

Usage

MultibodyComponents.PlanarMechanics.Prismatic(render=true, color=MultibodyComponents.world_default_prismatic_color(), specular_coefficient=1.5, r=[1, 0], box_width=MultibodyComponents.world_default_joint_width(), box_height=MultibodyComponents.world_default_joint_width(), z_position=0)

Parameters:

Name	Description	Units	Default value
statePriority		–	2
render		–	true
color		–	MultibodyCo...tic_color()
specular_coefficient		–	1.5
r	Direction of the rod wrt. body system at phi=0	m	[1, 0]
box_width	Half-width of the box in animations	–	MultibodyCo...int_width()
box_height	Half-height of the box in animations	–	MultibodyCo...int_width()
z_position	z-position of the box in animations	–	0

Connectors

• frame_a - Coordinate system (2-dim.) fixed to the component with one cut-force and cut-torque.

All variables are resolved in the planar world frame. (Frame2D)

• frame_b - Coordinate system (2-dim.) fixed to the component with one cut-force and cut-torque.

All variables are resolved in the planar world frame. (Frame2D)

Variables

Name	Description	Units
s	Joint coordinate	m
v		m/s
a		m/s2
f		N
e0		–
r0	Translation vector of the prismatic rod resolved w.r.t. inertial frame	m

Behavior

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

Source

"""
Prismatic (sliding) joint allowing translation along a fixed direction.

The sliding direction is given by parameter `r`, rotated by frame_a's orientation.
Without axisflange support, the joint slides freely (`f = 0`).
"""
component Prismatic
  extends PartialTwoFrames
  extends MultibodyComponents.Renderable(color = MultibodyComponents.world_default_prismatic_color())
  "Visualization shape for the prismatic rod"
  shape = MultibodyComponents.BoxShape(render = render, color = color, r_shape = [frame_a.x, frame_a.y, z_position], length_direction = [e0[1], e0[2], 0], width_direction = [0, 0, 1], length = s, width = box_width, height = box_height)
  structural parameter statePriority::Integer = 2
  "Direction of the rod wrt. body system at phi=0"
  parameter r::Length[2] = [1, 0]
  "Half-width of the box in animations"
  parameter box_width::Real = MultibodyComponents.world_default_joint_width()
  "Half-height of the box in animations"
  parameter box_height::Real = MultibodyComponents.world_default_joint_width()
  "z-position of the box in animations"
  parameter z_position::Real = 0
  "Joint coordinate"
  variable s::Length(statePriority = statePriority)
  variable v::Velocity(statePriority = statePriority)
  variable a::Acceleration
  variable f::Dyad.Force
  variable e0::Real[2]
  "Translation vector of the prismatic rod resolved w.r.t. inertial frame"
  variable r0::Length[2]
relations
  # Rotate the unit direction by frame_a angle
  e0 = [[cos(frame_a.phi), -sin(frame_a.phi)], [sin(frame_a.phi), cos(frame_a.phi)]] * (r / norm(r))
  r0 = e0 * s
  v = der(s)
  a = der(v)
  # position constraint
  frame_a.x + r0[1] = frame_b.x
  frame_a.y + r0[2] = frame_b.y
  # orientation rigidly transferred
  frame_a.phi = frame_b.phi
  # force balance
  frame_a.fx + frame_b.fx = 0
  frame_a.fy + frame_b.fy = 0
  # torque balance with lever arm
  frame_a.tau + frame_b.tau + r0[1] * frame_b.fy - r0[2] * frame_b.fx = 0
  # joint force along sliding direction
  e0[1] * frame_a.fx + e0[2] * frame_a.fy = f
  # free sliding (no axisflange)
  f = 0
metadata {"Dyad": {"icons": {"default": "dyad://MultibodyComponents/Prismatic.svg"}}}
end

Flattened Source

"""
Prismatic (sliding) joint allowing translation along a fixed direction.

The sliding direction is given by parameter `r`, rotated by frame_a's orientation.
Without axisflange support, the joint slides freely (`f = 0`).
"""
component Prismatic
  frame_a = Frame2D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 50, "y1": 450, "x2": 150, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  frame_b = Frame2D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 850, "y1": 450, "x2": 950, "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
  "Visualization shape for the prismatic rod"
  shape = MultibodyComponents.BoxShape(render = render, color = color, r_shape = [frame_a.x, frame_a.y, z_position], length_direction = [e0[1], e0[2], 0], width_direction = [0, 0, 1], length = s, width = box_width, height = box_height)
  structural parameter statePriority::Integer = 2
  "Direction of the rod wrt. body system at phi=0"
  parameter r::Length[2] = [1, 0]
  "Half-width of the box in animations"
  parameter box_width::Real = MultibodyComponents.world_default_joint_width()
  "Half-height of the box in animations"
  parameter box_height::Real = MultibodyComponents.world_default_joint_width()
  "z-position of the box in animations"
  parameter z_position::Real = 0
  "Joint coordinate"
  variable s::Length(statePriority = statePriority)
  variable v::Velocity(statePriority = statePriority)
  variable a::Acceleration
  variable f::Dyad.Force
  variable e0::Real[2]
  "Translation vector of the prismatic rod resolved w.r.t. inertial frame"
  variable r0::Length[2]
relations
  # Rotate the unit direction by frame_a angle
  e0 = [[cos(frame_a.phi), -sin(frame_a.phi)], [sin(frame_a.phi), cos(frame_a.phi)]] * (r / norm(r))
  r0 = e0 * s
  v = der(s)
  a = der(v)
  # position constraint
  frame_a.x + r0[1] = frame_b.x
  frame_a.y + r0[2] = frame_b.y
  # orientation rigidly transferred
  frame_a.phi = frame_b.phi
  # force balance
  frame_a.fx + frame_b.fx = 0
  frame_a.fy + frame_b.fy = 0
  # torque balance with lever arm
  frame_a.tau + frame_b.tau + r0[1] * frame_b.fy - r0[2] * frame_b.fx = 0
  # joint force along sliding direction
  e0[1] * frame_a.fx + e0[2] * frame_a.fy = f
  # free sliding (no axisflange)
  f = 0
metadata {"Dyad": {"icons": {"default": "dyad://MultibodyComponents/Prismatic.svg"}}}
end

Test Cases

No test cases defined.

Related

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