LIBRARY

Torque

Torque acting between two frames, defined by 3 input signals resolved in the frame specified by resolve_in_frame.

No force is transmitted, only torque. The torque balance ensures equal and opposite torques on frame_a and frame_b.

Usage

MultibodyComponents.Torque()

Parameters:

Name	Description	Units	Default value
resolve_in_frame		–	ResolveInFrame.FrameB()

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)

• torque_x - This connector represents a real signal as an input to a component (RealInput)

• torque_y - This connector represents a real signal as an input to a component (RealInput)

• torque_z - This connector represents a real signal as an input to a component (RealInput)

Variables

Name	Description	Units
r_0	Position vector from frame_a to frame_b in world frame	m
t_b_0	Torque at frame_b resolved in world frame	N.m

Behavior

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

Source

"""
Torque acting between two frames, defined by 3 input signals resolved in
the frame specified by `resolve_in_frame`.

No force is transmitted, only torque. The torque balance ensures
equal and opposite torques on `frame_a` and `frame_b`.
"""
component Torque
  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": []
    }
  }
  torque_x = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 90, "y1": -50, "x2": 190, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  torque_y = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -50, "x2": 550, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  torque_z = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 810, "y1": -50, "x2": 910, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  structural parameter resolve_in_frame::ResolveInFrame = ResolveInFrame.FrameB()
  "Position vector from frame_a to frame_b in world frame"
  variable r_0::Position[3]
  "Torque at frame_b resolved in world frame"
  variable t_b_0::Dyad.Torque[3]
relations
  r_0 = frame_b.r_0 - frame_a.r_0
  frame_a.f = [0, 0, 0]
  frame_b.f = [0, 0, 0]
  # Torque balance at frame_a (t_b_0 is the world-frame torque)
  frame_a.tau + resolve2(frame_a.R, t_b_0) = [0, 0, 0]
  switch resolve_in_frame
    case FrameA
      t_b_0 = -resolve1(frame_a.R, [torque_x, torque_y, torque_z])
      frame_b.tau = resolve2(frame_b.R, t_b_0)
    case FrameB
      t_b_0 = -resolve1(frame_b.R, [torque_x, torque_y, torque_z])
      frame_b.tau = -[torque_x, torque_y, torque_z]
    case World
      t_b_0 = -[torque_x, torque_y, torque_z]
      frame_b.tau = resolve2(frame_b.R, t_b_0)
  end
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/Torque.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 200,
        "rot": 0,
        "attrs": {"font-size": "140"}
      }
    ]
  }
}
end

Flattened Source

"""
Torque acting between two frames, defined by 3 input signals resolved in
the frame specified by `resolve_in_frame`.

No force is transmitted, only torque. The torque balance ensures
equal and opposite torques on `frame_a` and `frame_b`.
"""
component Torque
  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": []
    }
  }
  torque_x = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 90, "y1": -50, "x2": 190, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  torque_y = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -50, "x2": 550, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  torque_z = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 810, "y1": -50, "x2": 910, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  structural parameter resolve_in_frame::ResolveInFrame = ResolveInFrame.FrameB()
  "Position vector from frame_a to frame_b in world frame"
  variable r_0::Position[3]
  "Torque at frame_b resolved in world frame"
  variable t_b_0::Dyad.Torque[3]
relations
  r_0 = frame_b.r_0 - frame_a.r_0
  frame_a.f = [0, 0, 0]
  frame_b.f = [0, 0, 0]
  # Torque balance at frame_a (t_b_0 is the world-frame torque)
  frame_a.tau + resolve2(frame_a.R, t_b_0) = [0, 0, 0]
  switch resolve_in_frame
    case FrameA
      t_b_0 = -resolve1(frame_a.R, [torque_x, torque_y, torque_z])
      frame_b.tau = resolve2(frame_b.R, t_b_0)
    case FrameB
      t_b_0 = -resolve1(frame_b.R, [torque_x, torque_y, torque_z])
      frame_b.tau = -[torque_x, torque_y, torque_z]
    case World
      t_b_0 = -[torque_x, torque_y, torque_z]
      frame_b.tau = resolve2(frame_b.R, t_b_0)
  end
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/Torque.svg"},
    "labels": [
      {
        "label": "$(instance)",
        "x": 500,
        "y": 200,
        "rot": 0,
        "attrs": {"font-size": "140"}
      }
    ]
  }
}
end

Test Cases

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