RelativeSpeedSensor

Ideal sensor measuring the relative translational velocity between two mechanical flanges.

This component computes the relative translational velocity between two mechanical flanges, flange_a and flange_b. It first determines the relative displacement, s_rel, by subtracting the absolute position of flange_a from the absolute position of flange_b:

$$s_{rel}=flang{e}_b.s-flang{e}_a.s$$

The relative velocity, v_rel, is then calculated as the time derivative of this relative displacement:

$$v_{rel}=\frac{d(s_{rel})}{dt}$$

The sensor is ideal, meaning it does not exert any force on the connected flanges, which is enforced by the equation:

$$flang{e}_a.f=0$$

PartialRelativeSensor

Usage

RelativeSpeedSensor()

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)

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

Variables

Name	Description	Units
s_rel	Relative position of flange_b relative to flange_a	m

Behavior

$$\begin{array}{rl}0& =\mathtt{flange}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{f}\left(t\right)+\mathtt{flange}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{f}\left(t\right)\\ \mathtt{s}\mathtt{\_}\mathtt{rel}\left(t\right)& =\mathtt{flange}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{s}\left(t\right)-\mathtt{flange}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{s}\left(t\right)\\ \mathtt{v}\mathtt{\_}\mathtt{rel}\left(t\right)& =\frac{\mathrm{d}\mathtt{s}\mathtt{\_}\mathtt{rel}\left(t\right)}{\mathrm{d}t}\\ 0& =\mathtt{flange}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{f}\left(t\right)\end{array}$$

Source

# Ideal sensor measuring the relative translational velocity between two mechanical flanges.
#
# This component computes the relative translational velocity between two mechanical flanges, `flange_a` and `flange_b`.
# It first determines the relative displacement, `s_rel`, by subtracting the absolute position of `flange_a` from the absolute position of `flange_b`:
#
# ```math
# s_{rel} = flange_b.s - flange_a.s
# ```
#
# The relative velocity, `v_rel`, is then calculated as the time derivative of this relative displacement:
#
# ```math
# v_{rel} = \frac{d(s_{rel})}{dt}
# ```
#
# The sensor is ideal, meaning it does not exert any force on the connected flanges, which is enforced by the equation:
#
# ```math
# flange_a.f = 0
# ```
component RelativeSpeedSensor
  extends PartialRelativeSensor
  # Relative velocity of `flange_b` relative to `flange_a` as output signal
  v_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
relations
  s_rel = flange_b.s - flange_a.s
  v_rel = der(s_rel)
  0 = flange_a.f
metadata {
  "Dyad": {"icons": {"default": "dyad://TranslationalComponents/RelativeSensor.svg"}}
}
end

Flattened Source

# Ideal sensor measuring the relative translational velocity between two mechanical flanges.
#
# This component computes the relative translational velocity between two mechanical flanges, `flange_a` and `flange_b`.
# It first determines the relative displacement, `s_rel`, by subtracting the absolute position of `flange_a` from the absolute position of `flange_b`:
#
# ```math
# s_{rel} = flange_b.s - flange_a.s
# ```
#
# The relative velocity, `v_rel`, is then calculated as the time derivative of this relative displacement:
#
# ```math
# v_{rel} = \frac{d(s_{rel})}{dt}
# ```
#
# The sensor is ideal, meaning it does not exert any force on the connected flanges, which is enforced by the equation:
#
# ```math
# flange_a.f = 0
# ```
component RelativeSpeedSensor
  # 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 velocity of `flange_b` relative to `flange_a` as output signal
  v_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
relations
  0 = flange_a.f + flange_b.f
  s_rel = flange_b.s - flange_a.s
  v_rel = der(s_rel)
  0 = flange_a.f
metadata {
  "Dyad": {"icons": {"default": "dyad://TranslationalComponents/RelativeSensor.svg"}}
}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • RelativeSensorsTest