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.

This component extends from PartialElementaryRotationalToTranslational

Usage

RotationalComponents.RackAndPinion(radius)

Parameters:

Name	Description	Units	Default value
radius	Specifies the radius of the pinion gear, determining the kinematic relationship between rotational and translational motion.	m

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

$$\begin{array}{rl}\mathtt{radius}(-\mathtt{support}\mathtt{\_}\mathtt{r}\mathtt{.}\mathtt{phi}\left(t\right)+\mathtt{spline}\mathtt{.}\mathtt{phi}\left(t\right))& =\mathtt{flange}\mathtt{.}\mathtt{s}\left(t\right)-\mathtt{support}\mathtt{\_}\mathtt{t}\mathtt{.}\mathtt{s}\left(t\right)\\ 0& =\mathtt{spline}\mathtt{.}\mathtt{tau}\left(t\right)+\mathtt{radius}\mathtt{flange}\mathtt{.}\mathtt{f}\left(t\right)\end{array}$$

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

Flattened 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
  "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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