RelativeAngleSensor Icon

`RelativeAngleSensor`

Ideal sensor to measure the relative angle between two splines.

This component computes the difference between the angle of spline_b (denoted $\phib$) and the angle of `splinea(denoted \$\\phi_a\$). This difference is provided as the output signalphirel. It models an ideal sensor, ensuring it does not influence the dynamics of the connected mechanical system. This is achieved by enforcing that the torque exerted onsplinea` (denoted $\tau_a$) is zero. The governing equations are:

\[\\phi_{rel} = \\phi_b - \\phi_a\]

\[\tau_a = 0\]

PartialRelativeSensor

Usage

RelativeAngleSensor()

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

Behavior

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

Source

# Ideal sensor to measure the relative angle between two splines.
#
# This component computes the difference between the angle of `spline_b` (denoted \$\\phi_b\$)
# and the angle of `spline_a` (denoted \$\\phi_a\$). This difference is provided as the output
# signal `phi_rel`. It models an ideal sensor, ensuring it does not influence the
# dynamics of the connected mechanical system. This is achieved by enforcing that the
# torque exerted on `spline_a` (denoted \$\tau_a\$) is zero.
# The governing equations are:
# ```math
# \\phi_{rel} = \\phi_b - \\phi_a
# ```
# ```math
# \tau_a = 0
# ```
component RelativeAngleSensor
  extends PartialRelativeSensor
  # Relative angle between two splines as output signal
  phi_rel = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 90}}
    }
  }]
relations
  phi_rel = spline_b.phi-spline_a.phi
  0 = spline_a.tau
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/RelSensor-Angle-Vel-Acc.svg"}
  }
}
end

Flattened Source

# Ideal sensor to measure the relative angle between two splines.
#
# This component computes the difference between the angle of `spline_b` (denoted \$\\phi_b\$)
# and the angle of `spline_a` (denoted \$\\phi_a\$). This difference is provided as the output
# signal `phi_rel`. It models an ideal sensor, ensuring it does not influence the
# dynamics of the connected mechanical system. This is achieved by enforcing that the
# torque exerted on `spline_a` (denoted \$\tau_a\$) is zero.
# The governing equations are:
# ```math
# \\phi_{rel} = \\phi_b - \\phi_a
# ```
# ```math
# \tau_a = 0
# ```
component RelativeAngleSensor
  # 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}}}}]
  # Relative angle between two splines as output signal
  phi_rel = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 450, "y1": 950, "x2": 550, "y2": 1050, "rot": 90}}
    }
  }]
relations
  0 = spline_a.tau+spline_b.tau
  phi_rel = spline_b.phi-spline_a.phi
  0 = spline_a.tau
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/RelSensor-Angle-Vel-Acc.svg"}
  }
}
end

Test Cases

No test cases defined.

Examples
Experiments
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RelativeAngleSensor