RelativeAngleSensor

Ideal sensor to measure the relative angle between two splines.

This component computes the difference between the angle of spline_b (denoted $\varphi \ast b$) and the angle of spline*a(denoted ${\varphi }_a$). This difference is provided as the output signalphi*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 onspline*a (denoted \tau_a$) is zero. The governing equations are:

$$\begin{gathered} ph{i}_{rel}= \\ ph{i}_b- \\ ph{i}_a \end{gathered}$$$${\tau }_a=0$$

This component extends from PartialRelativeSensor

Usage

RotationalComponents.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

$$\begin{array}{rl}0& =\mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{tau}\left(t\right)+\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{tau}\left(t\right)\\ \mathtt{phi}\mathtt{\_}\mathtt{rel}\left(t\right)& =\mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{phi}\left(t\right)-\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{phi}\left(t\right)\\ 0& =\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{tau}\left(t\right)\end{array}$$

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.

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