LIBRARY

PlanarMechanics.TransformRelativeVector

Rotates a relative vector between frames via a two-step rotation through the world frame: input frame -> world -> output frame. Supports World, FrameA, FrameB, and FrameResolve. Angular quantities are frame-invariant in 2D so phi_out = phi_in when using the R1[3,3] matrix (no phi offset column).

Usage

MultibodyComponents.PlanarMechanics.TransformRelativeVector()

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_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)

• 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_in		–
r_out		–

Behavior

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

Source

"""
Rotates a relative vector between frames via a two-step rotation through the
world frame: input frame -> world -> output frame. Supports World, FrameA,
FrameB, and FrameResolve. Angular quantities are frame-invariant in 2D so
phi_out = phi_in when using the R1[3,3] matrix (no phi offset column).
"""
component TransformRelativeVector
  frame_a = Frame2D()
  frame_b = Frame2D()
  frame_resolve = Frame2D() if (frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()) or (frame_out == MultibodyComponents.ResolveInFrame.FrameResolve())
  x_in = RealInput()
  y_in = RealInput()
  phi_in = RealInput()
  x_out = RealOutput()
  y_out = RealOutput()
  phi_out = RealOutput()
  structural parameter frame_in::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  structural parameter frame_out::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  variable R1::Real[3, 3] if frame_out != frame_in
  variable rotation_matrix::Real[3, 3] if frame_out != frame_in
  variable r_in::Real[3] if frame_out != frame_in
  variable r_out::Real[3] if frame_out != frame_in
relations
  frame_a.fx = 0
  frame_a.fy = 0
  frame_a.tau = 0
  frame_b.fx = 0
  frame_b.fy = 0
  frame_b.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
    r_in = [x_in, y_in, phi_in]
    if frame_in == MultibodyComponents.ResolveInFrame.World()
      R1 = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameA()
      R1 = [[cos(frame_a.phi), -sin(frame_a.phi), 0], [sin(frame_a.phi), cos(frame_a.phi), 0], [0, 0, 1]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameB()
      R1 = [[cos(frame_b.phi), -sin(frame_b.phi), 0], [sin(frame_b.phi), cos(frame_b.phi), 0], [0, 0, 1]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()
      R1 = [[cos(frame_resolve.phi), -sin(frame_resolve.phi), 0], [sin(frame_resolve.phi), cos(frame_resolve.phi), 0], [0, 0, 1]]
    end
    if frame_out == MultibodyComponents.ResolveInFrame.World()
      rotation_matrix = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
      r_out = R1 * r_in
    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_out = transpose(rotation_matrix) * (R1 * r_in)
    end
    if frame_out == MultibodyComponents.ResolveInFrame.FrameB()
      rotation_matrix = [[cos(frame_b.phi), -sin(frame_b.phi), 0], [sin(frame_b.phi), cos(frame_b.phi), 0], [0, 0, 1]]
      r_out = transpose(rotation_matrix) * (R1 * r_in)
    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_out = transpose(rotation_matrix) * (R1 * r_in)
    end
    [x_out, y_out, phi_out] = r_out
  end
end

Flattened Source

"""
Rotates a relative vector between frames via a two-step rotation through the
world frame: input frame -> world -> output frame. Supports World, FrameA,
FrameB, and FrameResolve. Angular quantities are frame-invariant in 2D so
phi_out = phi_in when using the R1[3,3] matrix (no phi offset column).
"""
component TransformRelativeVector
  frame_a = Frame2D()
  frame_b = Frame2D()
  frame_resolve = Frame2D() if (frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()) or (frame_out == MultibodyComponents.ResolveInFrame.FrameResolve())
  x_in = RealInput()
  y_in = RealInput()
  phi_in = RealInput()
  x_out = RealOutput()
  y_out = RealOutput()
  phi_out = RealOutput()
  structural parameter frame_in::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  structural parameter frame_out::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
  variable R1::Real[3, 3] if frame_out != frame_in
  variable rotation_matrix::Real[3, 3] if frame_out != frame_in
  variable r_in::Real[3] if frame_out != frame_in
  variable r_out::Real[3] if frame_out != frame_in
relations
  frame_a.fx = 0
  frame_a.fy = 0
  frame_a.tau = 0
  frame_b.fx = 0
  frame_b.fy = 0
  frame_b.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
    r_in = [x_in, y_in, phi_in]
    if frame_in == MultibodyComponents.ResolveInFrame.World()
      R1 = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameA()
      R1 = [[cos(frame_a.phi), -sin(frame_a.phi), 0], [sin(frame_a.phi), cos(frame_a.phi), 0], [0, 0, 1]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameB()
      R1 = [[cos(frame_b.phi), -sin(frame_b.phi), 0], [sin(frame_b.phi), cos(frame_b.phi), 0], [0, 0, 1]]
    end
    if frame_in == MultibodyComponents.ResolveInFrame.FrameResolve()
      R1 = [[cos(frame_resolve.phi), -sin(frame_resolve.phi), 0], [sin(frame_resolve.phi), cos(frame_resolve.phi), 0], [0, 0, 1]]
    end
    if frame_out == MultibodyComponents.ResolveInFrame.World()
      rotation_matrix = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
      r_out = R1 * r_in
    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_out = transpose(rotation_matrix) * (R1 * r_in)
    end
    if frame_out == MultibodyComponents.ResolveInFrame.FrameB()
      rotation_matrix = [[cos(frame_b.phi), -sin(frame_b.phi), 0], [sin(frame_b.phi), cos(frame_b.phi), 0], [0, 0, 1]]
      r_out = transpose(rotation_matrix) * (R1 * r_in)
    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_out = transpose(rotation_matrix) * (R1 * r_in)
    end
    [x_out, y_out, phi_out] = r_out
  end
metadata {}
end

Test Cases

No test cases defined.

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