LIBRARY

PlanarMechanics.Power

Measures the mechanical power transmitted between two rigidly connected frames.

Power is computed as the sum of translational power (force · velocity) and rotational power (torque · angular velocity): power = frame_a.fx * der(frame_a.x) + frame_a.fy * der(frame_a.y) + frame_a.tau * der(frame_a.phi)

This is a sensor component: it constrains frame_a and frame_b to be identical and does not alter the dynamics of the system.

This component extends from PartialTwoFrameSensor

Usage

MultibodyComponents.PlanarMechanics.Power()

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)

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

Behavior

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

Source

"""
Measures the mechanical power transmitted between two rigidly connected frames.

Power is computed as the sum of translational power (force · velocity) and
rotational power (torque · angular velocity):
  power = frame_a.fx * der(frame_a.x) + frame_a.fy * der(frame_a.y) + frame_a.tau * der(frame_a.phi)

This is a sensor component: it constrains frame_a and frame_b to be identical
and does not alter the dynamics of the system.
"""
component Power
  extends PartialTwoFrameSensor
  "Mechanical power output"
  power = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 960, "x2": 550, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
relations
  # Rigid connection: identical position and orientation
  frame_a.x = frame_b.x
  frame_a.y = frame_b.y
  frame_a.phi = frame_b.phi
  # Force balance
  frame_a.fx + frame_b.fx = 0
  frame_a.fy + frame_b.fy = 0
  # Torque balance
  frame_a.tau + frame_b.tau = 0
  # Power = force · velocity + torque · angular velocity
  power = frame_a.fx * der(frame_a.x) + frame_a.fy * der(frame_a.y) + frame_a.tau * der(frame_a.phi)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/TwoFrameSensor.svg"},
    "labels": [{"label": "power", "x": 500, "y": 680, "rot": 0}]
  }
}
end

Flattened Source

"""
Measures the mechanical power transmitted between two rigidly connected frames.

Power is computed as the sum of translational power (force · velocity) and
rotational power (torque · angular velocity):
  power = frame_a.fx * der(frame_a.x) + frame_a.fy * der(frame_a.y) + frame_a.tau * der(frame_a.phi)

This is a sensor component: it constrains frame_a and frame_b to be identical
and does not alter the dynamics of the system.
"""
component Power
  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": []
    }
  }
  "Mechanical power output"
  power = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 450, "y1": 960, "x2": 550, "y2": 1060, "rot": 90}
      },
      "tags": []
    }
  }
relations
  # Rigid connection: identical position and orientation
  frame_a.x = frame_b.x
  frame_a.y = frame_b.y
  frame_a.phi = frame_b.phi
  # Force balance
  frame_a.fx + frame_b.fx = 0
  frame_a.fy + frame_b.fy = 0
  # Torque balance
  frame_a.tau + frame_b.tau = 0
  # Power = force · velocity + torque · angular velocity
  power = frame_a.fx * der(frame_a.x) + frame_a.fy * der(frame_a.y) + frame_a.tau * der(frame_a.phi)
metadata {
  "Dyad": {
    "icons": {"default": "dyad://MultibodyComponents/TwoFrameSensor.svg"},
    "labels": [{"label": "power", "x": 500, "y": 680, "rot": 0}]
  }
}
end

Test Cases

No test cases defined.

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