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RackAndPinion

Simple 1-dim. model of rack and pinion system without inertia. Rotational motion of circular gear (pinion) is converted to linear motion of linear gear (rack).

This component extends from IdealRollingWheel

Usage

RackAndPinion(radius)

Parameters:

NameDescriptionUnitsDefault value
radiusPinion radiusm

Connectors

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

# Simple 1-dim. model of rack and pinion system without inertia. Rotational motion
# of circular gear (pinion) is converted to linear motion of linear gear (rack).
component RackAndPinion
  extends IdealRollingWheel
  # Pinion radius
  parameter radius::Length
metadata {
  "JuliaSim": {"icons": {"default": "jsml://RotationalComponents/IdealRollingWheel.svg"}}
}
end
Flattened Source
# Simple 1-dim. model of rack and pinion system without inertia. Rotational motion
# of circular gear (pinion) is converted to linear motion of linear gear (rack).
component RackAndPinion
  # Rotational shaft
  spline = Spline() [{
    "JuliaSim": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}
  }]
  # Translational shaft
  flange = Flange() [{
    "JuliaSim": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}
  }]
  support_r = Spline() [{
    "JuliaSim": {"placement": {"icon": {"x1": 100, "y1": 950, "x2": 200, "y2": 1050}}}
  }]
  support_t = Flange() [{
    "JuliaSim": {"placement": {"icon": {"x1": 800, "y1": 950, "x2": 900, "y2": 1050}}}
  }]
  # wheel radius
  parameter radius::Length
relations
  (spline.phi-support_r.phi)*radius = flange.s-support_t.s
  0 = radius*flange.f+spline.tau
metadata {
  "JuliaSim": {"icons": {"default": "jsml://RotationalComponents/IdealRollingWheel.svg"}}
}
end

Test Cases

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