RackAndPinion

Models an ideal rack and pinion system, converting rotational motion to translational motion.

This component represents a one-dimensional, inertia-less rack and pinion mechanism. It establishes a kinematic relationship between the rotation of the pinion (circular gear) and the translation of the rack (linear gear). The core behavior is inherited from the IdealRollingWheel component. This model assumes no slip between the rack and pinion and neglects any inertial effects.

PartialElementaryRotationalToTranslational

Usage

RackAndPinion(radius)

Parameters:

Connectors

• spline - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
• flange - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)
• support_r - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
• support_t - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

Behavior

\[ \begin{align} \mathtt{radius} \left( - \mathtt{support\_r.phi}\left( t \right) + \mathtt{spline.phi}\left( t \right) \right) &= \mathtt{flange.s}\left( t \right) - \mathtt{support\_t.s}\left( t \right) \\ 0 &= \mathtt{spline.tau}\left( t \right) + \mathtt{radius} \mathtt{flange.f}\left( t \right) \end{align} \]

Source

# Models an ideal rack and pinion system, converting rotational motion to translational motion.
#
# This component represents a one-dimensional, inertia-less rack and pinion mechanism.
# It establishes a kinematic relationship between the rotation of the pinion
# (circular gear) and the translation of the rack (linear gear). The core behavior
# is inherited from the `IdealRollingWheel` component. This model assumes no slip
# between the rack and pinion and neglects any inertial effects.
component RackAndPinion
  extends PartialElementaryRotationalToTranslational
  # Specifies the radius of the pinion gear, determining the kinematic relationship between rotational and translational motion.
  parameter radius::Length
relations
  (spline.phi-support_r.phi)*radius = flange.s-support_t.s
  0 = radius*flange.f+spline.tau
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/IdealRollingWheel.svg"}}
}
end

# Models an ideal rack and pinion system, converting rotational motion to translational motion.
#
# This component represents a one-dimensional, inertia-less rack and pinion mechanism.
# It establishes a kinematic relationship between the rotation of the pinion
# (circular gear) and the translation of the rack (linear gear). The core behavior
# is inherited from the `IdealRollingWheel` component. This model assumes no slip
# between the rack and pinion and neglects any inertial effects.
component RackAndPinion
  # Primary rotational mechanical interface
  spline = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Primary translational mechanical interface
  flange = Flange() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Rotational mechanical support interface (e.g., for housing)
  support_r = Spline() [{"Dyad": {"placement": {"icon": {"x1": 100, "y1": 950, "x2": 200, "y2": 1050}}}}]
  # Translational mechanical support interface (e.g., for housing)
  support_t = Flange() [{"Dyad": {"placement": {"icon": {"x1": 800, "y1": 950, "x2": 900, "y2": 1050}}}}]
  # Specifies the radius of the pinion gear, determining the kinematic relationship between rotational and translational motion.
  parameter radius::Length
relations
  (spline.phi-support_r.phi)*radius = flange.s-support_t.s
  0 = radius*flange.f+spline.tau
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/IdealRollingWheel.svg"}}
}
end

Test Cases

No test cases defined.

Related

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