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Planetary Gear

Represent set of carrier, sun, planet, and ring gear wheels with specified ring-sun gear ratio




The Planetary Gear block represents a set of carrier, ring, planet, and sun gear wheels. A planetary gear set can be constructed from planet-planet and ring-planet gears. The ring and sun corotate with a fixed gear ratio and in opposite directions with respect to the carrier.

To model the planet's rotational inertia, connect an Inertia block to the optional planet connector port.

Axis Motions and Constraints

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

rCωC = rSωS+ rPωP , rC = rS + rP

rRωR = rCωC+ rPωP , rR = rC + rP

In terms of the ring-to-sun gear ratio gRS = rR/rS, the key effective kinematic constraint is

(1 + gRSC = ωS + gRS·ωR

The four degrees of freedom are reduced to two independent degrees of freedom.

The gear ratio is also the ratio of the number of teeth on each gear and the ratio of the torques in each axis, gRS = NR/NS = τRS.

    Warning:   All gear ratios must be strictly positive. If any gear ratio equals 0 or becomes negative at any time, a Simscape™ Driveline™ simulation stops with an error.

    The gear ratio gRS must be strictly greater than one.

Planetary Gear Set

Dialog Box and Parameters

Ring (R)/Sun (S) gear ratio

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.

Show planet connector port (P)

Selecting this check box makes the connector port for the planet gear visible and available for connection to other driveline blocks.

Use this connector port to connect an Inertia block if you want to model the planet gear's inertia. The default is unselected, with the planet gear's inertia neglected in the dynamics.


The drive_planetary_pic example illustrates the planetary gear with an animation.

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