RelativeVelocitySensor

Ideal sensor for measuring the relative angular velocity between two rotational splines.

This component models an ideal sensor that measures the relative angular velocity between two mechanical rotational splines, named spline_a and spline_b The relative angle, $\phi_{rel}$, is calculated as the difference between the absolute angles of these two splines:

\[\\phi_{rel} = \\phi_{b} - \\phi_{a}\]

The primary output, $w_{rel}$, which represents the relative angular velocity, is then determined by the time derivative of this relative angle:

\[w_{rel} = \frac{d\\phi_{rel}}{dt}\]

The sensor is considered ideal as it does not exert any torque on the splines it measures.

PartialRelativeSensor

Usage

RelativeVelocitySensor()

Connectors

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

Variables

Behavior

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

Source

# Ideal sensor for measuring the relative angular velocity between two rotational splines.
#
# This component models an ideal sensor that measures the relative angular velocity
# between two mechanical rotational splines, named `spline_a` and `spline_b`
# The relative angle, \$\\phi_{rel}\$, is calculated as the difference
# between the absolute angles of these two splines:
# ```math
# \\phi_{rel} = \\phi_{b} - \\phi_{a}
# ```
# The primary output, \$w_{rel}\$, which represents the relative angular velocity,
# is then determined by the time derivative of this relative angle:
# ```math
# w_{rel} = \frac{d\\phi_{rel}}{dt}
# ```
# The sensor is considered ideal as it does not exert any torque on the splines
# it measures.
component RelativeVelocitySensor
  extends PartialRelativeSensor
  # Output signal representing the relative angular velocity between spline_b and spline_a.
  w_rel = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 90}}
    }
  }]
  # Internal variable representing the relative angle between spline_b and spline_a.
  variable phi_rel::Angle
relations
  phi_rel = spline_b.phi-spline_a.phi
  w_rel = der(phi_rel)
  0 = spline_a.tau
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/RelSensor-Angle-Vel-Acc.svg"}
  }
}
end

# Ideal sensor for measuring the relative angular velocity between two rotational splines.
#
# This component models an ideal sensor that measures the relative angular velocity
# between two mechanical rotational splines, named `spline_a` and `spline_b`
# The relative angle, \$\\phi_{rel}\$, is calculated as the difference
# between the absolute angles of these two splines:
# ```math
# \\phi_{rel} = \\phi_{b} - \\phi_{a}
# ```
# The primary output, \$w_{rel}\$, which represents the relative angular velocity,
# is then determined by the time derivative of this relative angle:
# ```math
# w_{rel} = \frac{d\\phi_{rel}}{dt}
# ```
# The sensor is considered ideal as it does not exert any torque on the splines
# it measures.
component RelativeVelocitySensor
  # Left spline connector for the sensor.
  spline_a = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Right spline connector for the sensor.
  spline_b = Spline() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Output signal representing the relative angular velocity between spline_b and spline_a.
  w_rel = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 90}}
    }
  }]
  # Internal variable representing the relative angle between spline_b and spline_a.
  variable phi_rel::Angle
relations
  0 = spline_a.tau+spline_b.tau
  phi_rel = spline_b.phi-spline_a.phi
  w_rel = der(phi_rel)
  0 = spline_a.tau
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/RelSensor-Angle-Vel-Acc.svg"}
  }
}
end

Test Cases

No test cases defined.

Related

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