# Gear Constraint

Constraint that restricts body motion to rotation along tangent circles

## Library

Constraints & Drivers

## Description

The two Bodies connected by a Gear Constraint block are each restricted to turn relative to another along pitch circles centered at each body. The pitch circle centers are the origins of the Body coordinate systems (CSs) at which the Gear Constraint block is connected on either side. The pitch circles are tangent at one contact point.

Let r1, r2 be the radius vectors of the two pitch circles and ω1, ω2 the angular velocity vectors of the two bodies. The Gear Constraint requires that:

${\text{ω}}_{1}\text{x}{r}_{1}={\text{ω}}_{2}\text{x}{r}_{2}$

You specify the scalar radii r1, r2 of the pitch circles.

You must also connect the two Bodies connected by a Gear Constraint to a third, carrier Body by Revolute or Cylindrical Joints. (The third carrier body can be ground, but you must use two Ground blocks in this case, because a Ground has only one Body CS port. Both Grounds represent the same immobile body.) The constrained pair of Bodies rotate relative to one another about distinct rotational axes defined by the angular velocity vectors ω1, ω2. These axes do not have to be parallel.

Constraints restrict relative degrees of freedom (DoFs) between a pair of bodies. Locally in a machine, they replace a Joint as the expression of the DoFs. Globally, Constraint blocks must occur topologically in closed loops. Like Bodies connected to a Joint, the two Bodies connected to a Constraint are ordered as base and follower, fixing the direction of relative motion.

You can connect a Constraint & Driver Sensor to a Constraint block, but not a Driver Actuator. The Constraint & Driver Sensor measures the reaction forces/torques between the constrained bodies.

## Dialog Box and Parameters

The dialog has two active areas, Connection parameters and Parameters.

## Connection Parameters

The base (B)-follower (F) Body sequence determines the sense of positive motion. Positive rotation is the follower rotating in the right-handed sense about the rotation axis.

Current base

When you connect the base (B) connector port on the Gear Constraint block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Gear Constraint Base and Follower Body Connector Ports.

Current follower

When you connect the follower (F) connector port on the Gear Constraint block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Gear Constraint Base and Follower Body Connector Ports.

Number of sensor ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Constraint & Driver Sensor blocks to this Constraint. The default is `0`.

Gear Constraint Base and Follower Body Connector Ports

## Parameters

Enter a radius for the pitch circle centered at base Body CS. In the pull-down menu to the right, select units. The defaults are `1` and `m` (meters), respectively.

Enter a radius for the pitch circle centered at follower Body CS. In the pull-down menu to the right, select units. The defaults are `1` and `m` (meters), respectively.

## Example

A simple example of a valid part of a model with a Gear Constraint:

The Body CS origins CS2@Body1 and CS1@Body2 must be separated and oriented in such a way that the gear pitch circles are in contact and tangent at one point.