RelativeAccelerationSensor

Ideal sensor measuring the relative acceleration between two translational flanges.

This sensor determines the acceleration of flange_b with respect to flange_a (where s_a and s_b in the equations below refer to flange_a.s and flange_b.s respectively). It operates by first calculating the relative displacement, $s_{rel} = s_b - s_a$. This relative displacement is then differentiated with respect to time to obtain the relative velocity, $v_{rel} = \frac{d(s_{rel})}{dt}$. Finally, the relative velocity is differentiated with respect to time to yield the relative acceleration, $a_{rel} = \frac{d(v_{rel})}{dt}$. The sensor is ideal, meaning it does not exert any force on the connected components; specifically, the force at flange_a is defined as zero, ensuring no mechanical load is introduced by the sensor.

PartialRelativeSensor

Usage

RelativeAccelerationSensor()

Connectors

• flange_a - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)
• flange_b - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)
• a_rel - This connector represents a real signal as an output from a component (RealOutput)

Variables

Behavior

\[ \begin{align} 0 &= \mathtt{flange\_b.f}\left( t \right) + \mathtt{flange\_a.f}\left( t \right) \\ \mathtt{s\_rel}\left( t \right) &= \mathtt{flange\_b.s}\left( t \right) - \mathtt{flange\_a.s}\left( t \right) \\ \mathtt{v\_rel}\left( t \right) &= \frac{\mathrm{d} \mathtt{s\_rel}\left( t \right)}{\mathrm{d}t} \\ \mathtt{a\_rel}\left( t \right) &= \frac{\mathrm{d} \mathtt{v\_rel}\left( t \right)}{\mathrm{d}t} \\ 0 &= \mathtt{flange\_a.f}\left( t \right) \end{align} \]

Source

# Ideal sensor measuring the relative acceleration between two translational flanges.
#
# This sensor determines the acceleration of `flange_b` with respect to `flange_a`
# (where `s_a` and `s_b` in the equations below refer to `flange_a.s` and `flange_b.s`
# respectively). It operates by first calculating the relative displacement,
# $s_{rel} = s_b - s_a$. This relative displacement is then differentiated with
# respect to time to obtain the relative velocity, $v_{rel} = \frac{d(s_{rel})}{dt}$.
# Finally, the relative velocity is differentiated with respect to time to yield the
# relative acceleration, $a_{rel} = \frac{d(v_{rel})}{dt}$. The sensor is ideal,
# meaning it does not exert any force on the connected components; specifically, the force at
# `flange_a` is defined as zero, ensuring no mechanical load is introduced by the sensor.
component RelativeAccelerationSensor
  extends PartialRelativeSensor
  # Relative acceleration of `flange_b` relative to `flange_a` as output signal
  a_rel = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 90}}
    }
  }]
  # Relative position of `flange_b` relative to `flange_a`
  variable s_rel::Distance
  # Relative velocity of `flange_b` relative to `flange_a`
  variable v_rel::Velocity
relations
  s_rel = flange_b.s-flange_a.s
  v_rel = der(s_rel)
  a_rel = der(v_rel)
  0 = flange_a.f
metadata {
  "Dyad": {"icons": {"default": "dyad://TranslationalComponents/RelativeSensor.svg"}}
}
end

# Ideal sensor measuring the relative acceleration between two translational flanges.
#
# This sensor determines the acceleration of `flange_b` with respect to `flange_a`
# (where `s_a` and `s_b` in the equations below refer to `flange_a.s` and `flange_b.s`
# respectively). It operates by first calculating the relative displacement,
# $s_{rel} = s_b - s_a$. This relative displacement is then differentiated with
# respect to time to obtain the relative velocity, $v_{rel} = \frac{d(s_{rel})}{dt}$.
# Finally, the relative velocity is differentiated with respect to time to yield the
# relative acceleration, $a_{rel} = \frac{d(v_{rel})}{dt}$. The sensor is ideal,
# meaning it does not exert any force on the connected components; specifically, the force at
# `flange_a` is defined as zero, ensuring no mechanical load is introduced by the sensor.
component RelativeAccelerationSensor
  # Negative connection flange of the sensor, often considered the reference point.
  flange_a = Flange() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Positive connection flange of the sensor, where the measurement is taken relative to flange_a.
  flange_b = Flange() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Relative acceleration of `flange_b` relative to `flange_a` as output signal
  a_rel = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 90}}
    }
  }]
  # Relative position of `flange_b` relative to `flange_a`
  variable s_rel::Distance
  # Relative velocity of `flange_b` relative to `flange_a`
  variable v_rel::Velocity
relations
  0 = flange_a.f+flange_b.f
  s_rel = flange_b.s-flange_a.s
  v_rel = der(s_rel)
  a_rel = der(v_rel)
  0 = flange_a.f
metadata {
  "Dyad": {"icons": {"default": "dyad://TranslationalComponents/RelativeSensor.svg"}}
}
end

Test Cases

No test cases defined.

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  • RelativeSensorsTest