SimMechanics    
Gear Constraint

Constrain the rotational motion of two bodies to move along tangent pitch 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 radii of the two pitch circles and 1, 2 the angular velocities of the two bodies. The Gear Constraint requires that:

You specify the 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 constrained pair of Bodies rotate relative to one another about distinct rotational axes. 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 block to a Constraint & Driver Sensor, but not to an Actuator. The Constraint & Driver Sensor measures the reaction forces/torques between the constrained bodies.

Dialog Box and Parameters

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

Connection Parameters

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 Gear Constraint base and follower Body Connector Ports figure.
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 Gear Constraint base and follower Body Connector Ports figure.
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.

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.

Gear Constraint base and follower Body Connector Ports

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.

Parameters

Pitch circle located at base
Enter Radius and Units for the pitch circle centered at base Body CS. The defaults are 1 and m (meters).
Pitch circle located at follower
Enter Radius and Units for the pitch circle centered at follower Body CS. The defaults are 1 and m (meters).

See Also

Constraint & Driver Sensor, Cylindrical, Revolute

See Modeling Constraints and Drivers for more on restricting DoFs with Constraints.

See Checking Schematic Topology and How SimMechanics Works for more on using constraints in closed loops.

See Creating Constraints and Drivers.


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