LIBRARY

PlanarMechanics.TransformAbsoluteVector

Rotates an absolute vector between frames via a two-step rotation through the world frame: input frame -> world -> output frame. Supports World, FrameA, and FrameResolve. Uses the R1[3,4] matrix approach from Multibody.jl to handle both rotational and translational (phi offset) components.

Usage

MultibodyComponents.PlanarMechanics.TransformAbsoluteVector()

Parameters:

Name	Description	Units	Default value
frame_in		–	MultibodyComponents.ResolveInFrame.FrameA()
frame_out		–	MultibodyComponents.ResolveInFrame.FrameA()

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_resolve - 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)

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

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

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

• x_out - This connector represents a real signal as an output from a component (RealOutput)

• y_out - This connector represents a real signal as an output from a component (RealOutput)

• phi_out - This connector represents a real signal as an output from a component (RealOutput)

Variables

Name	Description	Units
R1		–
rotation_matrix		–
r_temp		–
r		–

Behavior

$$\begin{array}{rl}\mathtt{frame}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{fx}\left(t\right)& =0\\ \mathtt{frame}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{fy}\left(t\right)& =0\\ \mathtt{frame}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{tau}\left(t\right)& =0\\ \mathtt{x}\mathtt{\_}\mathtt{out}\left(t\right)& =\mathtt{x}\mathtt{\_}\mathtt{in}\left(t\right)\\ \mathtt{y}\mathtt{\_}\mathtt{out}\left(t\right)& =\mathtt{y}\mathtt{\_}\mathtt{in}\left(t\right)\\ \mathtt{phi}\mathtt{\_}\mathtt{out}\left(t\right)& =\mathtt{phi}\mathtt{\_}\mathtt{in}\left(t\right)\end{array}$$

Source

"""
Rotates an absolute vector between frames via a two-step rotation through the
world frame: input frame -> world -> output frame. Supports World, FrameA,
and FrameResolve. Uses the R1[3,4] matrix approach from Multibody.jl to handle
both rotational and translational (phi offset) components.
"""
component TransformAbsoluteVector
  frame_a = Frame2D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 0}
      },
      "tags": []
    }
  }
  frame_resolve = Frame2D() if (frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()) or (frame_out == MultibodyComponents.ResolveInFrame.FrameResolve()) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -40, "x2": 550, "y2": 60, "rot": 0}
      },
      "tags": []
    }
  }
  x_in = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 140, "x2": 60, "y2": 240, "rot": 0}
      },
      "tags": []
    }
  }
  y_in = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 450, "x2": 60, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  phi_in = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 760, "x2": 60, "y2": 860, "rot": 0}
      },
      "tags": []
    }
  }
  x_out = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 140, "x2": 1060, "y2": 240, "rot": 0}
      },
      "tags": []
    }
  }
  y_out = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 450, "x2": 1060, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  phi_out = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 770, "x2": 1060, "y2": 870, "rot": 0}
      },
      "tags": []
    }
  }
  structural parameter frame_in::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  structural parameter frame_out::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  variable R1::Real[3, 4] if frame_out != frame_in
  variable rotation_matrix::Real[3, 3] if frame_out != frame_in
  variable r_temp::Real[3] if frame_out != frame_in
  variable r::Real[3] if frame_out != frame_in
relations
  frame_a.fx = 0
  frame_a.fy = 0
  frame_a.tau = 0
  if (frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()) or (frame_out == MultibodyComponents.ResolveInFrame.FrameResolve())
    frame_resolve.fx = 0
    frame_resolve.fy = 0
    frame_resolve.tau = 0
  end
  if frame_out == frame_in
    x_out = x_in
    y_out = y_in
    phi_out = phi_in
  else
    if frame_in == MultibodyComponents.ResolveInFrame.World()
      R1 = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameA()
      R1 = [[cos(frame_a.phi), -sin(frame_a.phi), 0, 0], [sin(frame_a.phi), cos(frame_a.phi), 0, 0], [0, 0, 1, frame_a.phi]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()
      R1 = [[cos(frame_resolve.phi), -sin(frame_resolve.phi), 0, 0], [sin(frame_resolve.phi), cos(frame_resolve.phi), 0, 0], [0, 0, 1, frame_resolve.phi]]
    end
    r_temp = R1 * [x_in, y_in, phi_in, 1]
    if frame_out == MultibodyComponents.ResolveInFrame.World()
      rotation_matrix = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
      r = r_temp
    end
    if frame_out == MultibodyComponents.ResolveInFrame.FrameA()
      rotation_matrix = [[cos(frame_a.phi), sin(frame_a.phi), 0], [-sin(frame_a.phi), cos(frame_a.phi), 0], [0, 0, 1]]
      r = rotation_matrix * r_temp
    end
    if frame_out == MultibodyComponents.ResolveInFrame.FrameResolve()
      rotation_matrix = [[cos(frame_resolve.phi), sin(frame_resolve.phi), 0], [-sin(frame_resolve.phi), cos(frame_resolve.phi), 0], [0, 0, 1]]
      r = rotation_matrix * r_temp
    end
    [x_out, y_out, phi_out] = r
  end
end

Flattened Source

"""
Rotates an absolute vector between frames via a two-step rotation through the
world frame: input frame -> world -> output frame. Supports World, FrameA,
and FrameResolve. Uses the R1[3,4] matrix approach from Multibody.jl to handle
both rotational and translational (phi offset) components.
"""
component TransformAbsoluteVector
  frame_a = Frame2D() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 0}
      },
      "tags": []
    }
  }
  frame_resolve = Frame2D() if (frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()) or (frame_out == MultibodyComponents.ResolveInFrame.FrameResolve()) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -40, "x2": 550, "y2": 60, "rot": 0}
      },
      "tags": []
    }
  }
  x_in = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 140, "x2": 60, "y2": 240, "rot": 0}
      },
      "tags": []
    }
  }
  y_in = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 450, "x2": 60, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  phi_in = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -40, "y1": 760, "x2": 60, "y2": 860, "rot": 0}
      },
      "tags": []
    }
  }
  x_out = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 140, "x2": 1060, "y2": 240, "rot": 0}
      },
      "tags": []
    }
  }
  y_out = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 450, "x2": 1060, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  phi_out = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 960, "y1": 770, "x2": 1060, "y2": 870, "rot": 0}
      },
      "tags": []
    }
  }
  structural parameter frame_in::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  structural parameter frame_out::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  variable R1::Real[3, 4] if frame_out != frame_in
  variable rotation_matrix::Real[3, 3] if frame_out != frame_in
  variable r_temp::Real[3] if frame_out != frame_in
  variable r::Real[3] if frame_out != frame_in
relations
  frame_a.fx = 0
  frame_a.fy = 0
  frame_a.tau = 0
  if (frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()) or (frame_out == MultibodyComponents.ResolveInFrame.FrameResolve())
    frame_resolve.fx = 0
    frame_resolve.fy = 0
    frame_resolve.tau = 0
  end
  if frame_out == frame_in
    x_out = x_in
    y_out = y_in
    phi_out = phi_in
  else
    if frame_in == MultibodyComponents.ResolveInFrame.World()
      R1 = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameA()
      R1 = [[cos(frame_a.phi), -sin(frame_a.phi), 0, 0], [sin(frame_a.phi), cos(frame_a.phi), 0, 0], [0, 0, 1, frame_a.phi]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()
      R1 = [[cos(frame_resolve.phi), -sin(frame_resolve.phi), 0, 0], [sin(frame_resolve.phi), cos(frame_resolve.phi), 0, 0], [0, 0, 1, frame_resolve.phi]]
    end
    r_temp = R1 * [x_in, y_in, phi_in, 1]
    if frame_out == MultibodyComponents.ResolveInFrame.World()
      rotation_matrix = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
      r = r_temp
    end
    if frame_out == MultibodyComponents.ResolveInFrame.FrameA()
      rotation_matrix = [[cos(frame_a.phi), sin(frame_a.phi), 0], [-sin(frame_a.phi), cos(frame_a.phi), 0], [0, 0, 1]]
      r = rotation_matrix * r_temp
    end
    if frame_out == MultibodyComponents.ResolveInFrame.FrameResolve()
      rotation_matrix = [[cos(frame_resolve.phi), sin(frame_resolve.phi), 0], [-sin(frame_resolve.phi), cos(frame_resolve.phi), 0], [0, 0, 1]]
      r = rotation_matrix * r_temp
    end
    [x_out, y_out, phi_out] = r
  end
metadata {}
end

Test Cases

No test cases defined.

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