Rack and pinion

Ideal rack and pinion: rotation to translation by a fixed ratio.

  • rotational
  • translational
  • Modelica Standard Library
  • 2 ports
  • 1 parameter
BlockRack and pinionKindgearR2TLibraryRotational

Description

An ideal rack and pinion, or any ideal rotary-to-linear transmission. The rotational flange turns ratio radians per meter of travel of the translational flange.

Example

Wheel and rack A wheel turns axle torque into force on a vehicle mass, and a rack and pinion turns speed into travel.

30 N·mWheel 0.1 kg·m²Wheel r 0.3 mVehicle 100 kgDrag 10 N·s/mRoadVehicle speedPinion 10 rad/sRack and pinionRack 1 kgRack position
In Gradara, select a Rack and pinion block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:Inertia (ideal)Rolling wheelConstant torqueConstant speedFixed (translational)MassDamperPosition sensorVelocity sensor

Ports

Conserving terminals 2

  • rotflangeRrotational

    Rotational flange (the pinion). Torque into it is positive.

  • linflangeTtranslational

    Translational flange (the rack). Force into it is positive.

Parameters

  • Ratioratio100 rad/m

    Transmission ratio flangeR.phi/flangeT.s, in rad/m. For a pinion of radius r, ratio = 1/r. A negative value reverses direction.

Equations

Modelica
flangeR.phi = ratio · flangeT.s
0 = ratio · flangeR.tau + flangeT.f

Implementation

Modelica Standard Library 4.1.0Modelica.Mechanics.Rotational.Components.IdealGearR2T
MSL documentation

Assumptions and limitations

  • No mass, inertia, friction, backlash, or elasticity.

See also

Select a block in Gradara and press F1 to open its page offline.