Planetary Gear

High-ratio gear reduction mechanism with sun, planet, and ring gears




This block represents a high-ratio gear reduction mechanism with four key components:

  • Sun gear

  • Planet Gear Set

  • Planet Gear Carrier

  • Ring Gear

The centrally located sun gear engages the planet gear set, which in turn engages the ring gear. A carrier holds the planet gear set. Each of these components, with the exception of the planet gear set, connects to a drive shaft.

Depending on which shaft is driving, driven, or fixed, the planetary gear train can achieve a variety of speed reduction ratios. These ratios are a function of the sun and ring radii, and therefore of their tooth numbers. You specify the tooth numbers directly in the block dialog box.

This block is a composite component with two underlying blocks:

The figure shows the connections between the two blocks.

Dialog Box and Parameters


Ring (R) to sun (S) teeth ratio (NR/NS)

Ratio gRS of the ring gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1. The default is 2.

Meshing Losses

Friction model

Select how to implement friction losses from nonideal meshing of gear teeth. The default is No meshing losses.

  • No meshing losses — Suitable for HIL simulation — Gear meshing is ideal.

  • Constant efficiency — Transfer of torque between gear wheel pairs is reduced by a constant efficiency η satisfying 0 < η ≤ 1. If you select this option, the panel changes from its default.

     Constant Efficiency

Viscous Losses

Sun-carrier and planet-carrier viscous friction coefficients

Vector of viscous friction coefficients [μS μP] for the sun-carrier and planet-carrier gear motions, respectively. The default is [0 0].

From the drop-down list, choose units. The default is newton-meters/(radians/second) (N*m/(rad/s)).

Planetary Gear Model

Ideal Gear Constraints and Gear Ratios

Planetary Gear imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal gear (planet):

rCωC = rSωS+ rPωP , rC = rS + rP ,

rRωR = rCωC+ rPωP , rR = rC + rP .

The ring-sun gear ratio gRS = rR/rS = NR/NS. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

(1 + gRSC = ωS + gRSωR .

The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (S,P) and (P,R).

    Warning   The gear ratio gRS must be strictly greater than one.

The torque transfer is:

gRSτS + τRτloss = 0 ,

with τloss = 0 in the ideal case.

Nonideal Gear Constraints and Losses

In the nonideal case, τloss ≠ 0. See Model Gears with Losses.


  • Gear inertia is negligible. It does not impact gear dynamics.

  • Gears are rigid. They do not deform.

  • Coulomb friction slows down simulation. See Adjust Model Fidelity.


CConserving rotational port that represents the planet gear carrier
RConserving rotational port that represents the ring gear
SConserving rotational port that represents the sun gear

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