AccelerationSensor

Measures the absolute angular acceleration of a rotational spline.

This sensor determines the absolute angular acceleration of its spline connector, leveraging properties inherited from PartialAbsoluteSensor, such as the spline's angle (spline.phi). The absolute angular velocity (w) is first calculated as the time derivative of this angle:

\[w = \frac{d\text{spline}.\\phi}{dt}\]

Then, the absolute angular acceleration (a) is computed as the time derivative of the angular velocity:

\[a = \frac{dw}{dt} = \frac{d^2\text{spline}.\\phi}{dt^2}\]

This resulting acceleration is provided as the output a.

This component extends from PartialAbsoluteSensor

Usage

RotationalComponents.AccelerationSensor()

Connectors

• spline - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
• a - This connector represents a real signal as an output from a component (RealOutput)

Variables

Behavior

\[ \begin{align} 0 &= \mathtt{spline.tau}\left( t \right) \\ w\left( t \right) &= \frac{\mathrm{d} \mathtt{spline.phi}\left( t \right)}{\mathrm{d}t} \\ a\left( t \right) &= \frac{\mathrm{d} w\left( t \right)}{\mathrm{d}t} \end{align} \]

Source

# Measures the absolute angular acceleration of a rotational spline.
#
# This sensor determines the absolute angular acceleration of its `spline` connector, leveraging properties inherited from `PartialAbsoluteSensor`, such as the spline's angle (`spline.phi`).
# The absolute angular velocity (`w`) is first calculated as the time derivative of this angle:
# ```math
# w = \frac{d\text{spline}.\\phi}{dt}
# ```
# Then, the absolute angular acceleration (`a`) is computed as the time derivative of the angular velocity:
# ```math
# a = \frac{dw}{dt} = \frac{d^2\text{spline}.\\phi}{dt^2}
# ```
# This resulting acceleration is provided as the output `a`.
component AccelerationSensor
  extends PartialAbsoluteSensor
  # Absolute angular acceleration of flange as output signal
  a = RealOutput() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Absolute angular velocity of flange
  variable w::AngularVelocity
relations
  w = der(spline.phi)
  a = der(w)
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/SingleSplineSensor.svg"}}
}
end

# Measures the absolute angular acceleration of a rotational spline.
#
# This sensor determines the absolute angular acceleration of its `spline` connector, leveraging properties inherited from `PartialAbsoluteSensor`, such as the spline's angle (`spline.phi`).
# The absolute angular velocity (`w`) is first calculated as the time derivative of this angle:
# ```math
# w = \frac{d\text{spline}.\\phi}{dt}
# ```
# Then, the absolute angular acceleration (`a`) is computed as the time derivative of the angular velocity:
# ```math
# a = \frac{dw}{dt} = \frac{d^2\text{spline}.\\phi}{dt^2}
# ```
# This resulting acceleration is provided as the output `a`.
component AccelerationSensor
  # Spline of the shaft from which sensor information shall be measured
  spline = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Absolute angular acceleration of flange as output signal
  a = RealOutput() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Absolute angular velocity of flange
  variable w::AngularVelocity
relations
  0 = spline.tau
  w = der(spline.phi)
  a = der(w)
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/SingleSplineSensor.svg"}}
}
end

Test Cases

No test cases defined.

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