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

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 - (Spline)

• flange - (Flange)

• support_r - (Spline)

• support_t - (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

This is setup code, that must be run before each test case.

using RotationalComponents
using ModelingToolkit, OrdinaryDiffEqDefault
using Plots
using CSV, DataFrames

snapshotsdir = joinpath(dirname(dirname(pathof(RotationalComponents))), "test", "snapshots")

"/home/actions-runner-10/.julia/packages/RotationalComponents/0VPxm/test/snapshots"

Related

• Examples

• Experiments

• Analyses