# Common Gear Constraint

Kinematic constraint between two coplanar spur gear bodies with parallel rotation axes

• Library:
• Simscape / Multibody / Gears and Couplings / Gears

## Description

The Common Gear Constraint block represents a kinematic constraint between two coplanar spur gear bodies with parallel rotation axes. The gear meshing can be external to both gears or internal to one of the gears. The base and follower frame ports identify the connection frames on the spur gear bodies. The gear rotation axes coincide with the frame z-axes.

The block represents only the kinematic constraint characteristic to a spur gear system. Gear inertia and geometry are solid properties that you must specify using solid blocks. The gear constraint model is ideal. Backlash and gear losses due to Coulomb and viscous friction between teeth are ignored. You can, however, model viscous friction at joints by specifying damping coefficients in the joint blocks.

### Gear Geometry

The common gear constraint is parameterized in terms of the dimensions of the gear pitch circles. A pitch circle is an imaginary circle concentric with the gear body and tangent to the tooth contact point. The pitch radii, labeled `RB` and `RF` in the figure, are the radii that the gears would have if they were reduced to friction cylinders in mutual contact.

### Gear Assembly

Gear constraints occur in closed kinematic loops. The figure shows the closed-loop topology of a simple common gear model. Joint blocks connect the gear bodies to a common fixture or carrier, defining the maximum degrees of freedom between them. A Common Gear Constraint block connects the gear bodies, eliminating one degree of freedom and effectively coupling the two gear motions.

### Assembly Requirements

The block imposes special restrictions on the relative positions and orientations of the gear connection frames. The restrictions ensure that the gears assemble only at distances and angles suitable for meshing. The block enforces the restrictions during model assembly, when it first attempts to place the gears in mesh, but relies on the remainder of the model to keep the gears in mesh during simulation.

Position Restrictions

• The distance between the z-axes of the base and follower frame, denoted dB-F in the figure, must equal the distance between the gear centers. This constraint ensures that the rotation axes of the gears are at the proper distance for meshing.

• The follower frame origin must lie on the xy plane of the base frame. This constraint ensures that the pitch circle of one gear is coplanar with the pitch circle of the other.

Orientation Restrictions

• The z-axes of the base and follower frames must point in the same direction. This constraint ensures that the gear rotation axes are parallel to each other. The figure shows the z-axes of the base and follower frames pointing out of the screen.

## Ports

### Frame

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Connection frame on the base gear body.

Connection frame on the follower gear body.

## Parameters

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Type of meshing between the base and follower gear bodies. Select `External` if both gears have outward-facing teeth. Select `Internal` if one gear has inward-facing teeth. Such a gear is known as a ring gear. The gear with the greater pitch radius serves as the ring gear.

Distance between the centers of the base and follower gear bodies. This distance is the sum of the base and follower gear pitch radii.

#### Dependencies

This parameter is enabled when the Specification Method parameter is set to ```Center Distance and Ratio```.

Number of follower gear teeth divided by the number of base gear teeth. The block uses this ratio to determine the speed and torque transmitted between the base and follower gear shafts.

#### Dependencies

This parameter is enabled when the Specification Method parameter is set to ```Center Distance and Ratio```.

Radius of the pitch circle of the base gear body. The pitch circle is an imaginary circle concentric with the gear body and tangent to the tooth contact point.

#### Dependencies

This parameter is enabled when the Specification Method parameter is set to ```Pitch Circle Radii```.

Radius of the pitch circle of the follower gear body. The pitch circle is an imaginary circle concentric with the gear body and tangent to the tooth contact point.

#### Dependencies

This parameter is enabled when the Specification Method parameter is set to ```Pitch Circle Radii```.

## Version History

Introduced in R2013a