LIBRARY

PlanarMechanics.RelativePosition

Measures relative position and orientation between the origins of two frame connectors.

Computes frame_b - frame_a. This is a sensor component: it reads kinematic quantities without exerting forces. Use connect to attach to body frames (sensor forces are zero, so the force balance is unaffected).

This component extends from PartialTwoFrameSensor

Usage

MultibodyComponents.PlanarMechanics.RelativePosition()

Parameters:

Name	Description	Units	Default value
resolve_in_frame		–	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)

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

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

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

Behavior

$$\left[\begin{array}{c}{\mathtt{rel}}_{\mathrm{x}}\left(t\right)={\mathtt{pos}\mathtt{.}\mathtt{rel}}_{\mathrm{x}}\left(t\right)\\ {\mathtt{rel}}_{\mathrm{y}}\left(t\right)={\mathtt{pos}\mathtt{.}\mathtt{rel}}_{\mathrm{y}}\left(t\right)\\ {\mathtt{rel}}_{\mathrm{phi}}\left(t\right)={\mathtt{pos}\mathtt{.}\mathtt{rel}}_{\mathrm{phi}}\left(t\right)\\ \mathrm{connect}(fram{e}_a,po{s}_{+}fram{e}_a)\\ \mathrm{connect}(fram{e}_b,po{s}_{+}fram{e}_b)\\ {\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{fx}}\left(t\right)=0\\ {\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{fy}}\left(t\right)=0\\ {\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{tau}}\left(t\right)=0\\ {\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{b}.\mathrm{fx}}\left(t\right)=0\\ {\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{b}.\mathrm{fy}}\left(t\right)=0\\ {\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{b}.\mathrm{tau}}\left(t\right)=0\\ {\mathrm{array}}_{literal}(\left[\begin{array}{c}3\end{array}\right],{\mathtt{pos}\mathtt{.}\mathtt{rel}}_{\mathrm{x}}\left(t\right),{\mathtt{pos}\mathtt{.}\mathtt{rel}}_{\mathrm{y}}\left(t\right),{\mathtt{pos}\mathtt{.}\mathtt{rel}}_{\mathrm{phi}}\left(t\right))=\mathtt{pos}\mathtt{.}\mathtt{r}\left(t\right)\\ {\mathtt{pos}\mathtt{.}\mathtt{rotation}}_{\mathrm{matrix}}\left(t\right)={\mathrm{array}}_{literal}(\left[\begin{array}{c}3\\ 3\end{array}\right],\cos \left({\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{phi}}\left(t\right)\right),\sin \left({\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{phi}}\left(t\right)\right),0,-\sin \left({\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{phi}}\left(t\right)\right),\cos \left({\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{phi}}\left(t\right)\right),0,0,0,1)\\ \mathtt{pos}\mathtt{.}\mathtt{r}\left(t\right)=\mathrm{transpose}\left({\mathtt{pos}\mathtt{.}\mathtt{rotation}}_{\mathrm{matrix}}\left(t\right)\right)\cdot {\mathrm{array}}_{literal}(\left[\begin{array}{c}3\end{array}\right],-{\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{x}}\left(t\right)+{\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{b}.\mathrm{x}}\left(t\right),{\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{b}.\mathrm{y}}\left(t\right)-{\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{y}}\left(t\right),-{\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{a}.\mathrm{phi}}\left(t\right)+{\mathtt{pos}\mathtt{.}\mathtt{frame}}_{\mathrm{b}.\mathrm{phi}}\left(t\right))\end{array}\right]$$

Source

"""
Measures relative position and orientation between the origins of two frame connectors.

Computes frame_b - frame_a. This is a sensor component: it reads kinematic quantities
without exerting forces. Use `connect` to attach to body frames (sensor forces are zero,
so the force balance is unaffected).
"""
component RelativePosition
  extends PartialTwoFrameSensor
  frame_resolve = Frame2D() if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameResolve() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -50, "x2": 550, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  "Relative x-position"
  rel_x = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 120, "y1": 960, "x2": 220, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "Relative y-position"
  rel_y = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 960, "x2": 550, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "Relative rotation angle (counterclockwise)"
  rel_phi = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 780, "y1": 960, "x2": 880, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  pos = BasicRelativePosition(resolve_in_frame = resolve_in_frame)
  structural parameter resolve_in_frame::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
relations
  connect(frame_a, pos.frame_a)
  connect(frame_b, pos.frame_b)
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameResolve()
    connect(frame_resolve, pos.frame_resolve)
  end
  rel_x = pos.rel_x
  rel_y = pos.rel_y
  rel_phi = pos.rel_phi
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/TwoFrameSensor.svg"},
    "labels": [{"label": "rel pos", "x": 500, "y": 680, "rot": 0}]
  }
}
end

Flattened Source

"""
Measures relative position and orientation between the origins of two frame connectors.

Computes frame_b - frame_a. This is a sensor component: it reads kinematic quantities
without exerting forces. Use `connect` to attach to body frames (sensor forces are zero,
so the force balance is unaffected).
"""
component RelativePosition
  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": []
    }
  }
  frame_resolve = Frame2D() if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameResolve() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": -50, "x2": 550, "y2": 50, "rot": 0}
      },
      "tags": []
    }
  }
  "Relative x-position"
  rel_x = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 120, "y1": 960, "x2": 220, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "Relative y-position"
  rel_y = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 960, "x2": 550, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  "Relative rotation angle (counterclockwise)"
  rel_phi = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 780, "y1": 960, "x2": 880, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
  pos = BasicRelativePosition(resolve_in_frame = resolve_in_frame)
  structural parameter resolve_in_frame::MultibodyComponents.ResolveInFrame = MultibodyComponents.ResolveInFrame.FrameA()
relations
  connect(frame_a, pos.frame_a)
  connect(frame_b, pos.frame_b)
  if resolve_in_frame == MultibodyComponents.ResolveInFrame.FrameResolve()
    connect(frame_resolve, pos.frame_resolve)
  end
  rel_x = pos.rel_x
  rel_y = pos.rel_y
  rel_phi = pos.rel_phi
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/TwoFrameSensor.svg"},
    "labels": [{"label": "rel pos", "x": 500, "y": 680, "rot": 0}]
  }
}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

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• Tests

  • SensorsTest