# Constraint: Gear

Model ElementConstraint_Gear defines a gear constraint between two bodies.

## Description

The gear is modeled as an algebraic relationship between input and output displacements between two joints. The inputs and outputs may be either rotational or translational. This allows spur, helical, bevel, and rack-and-pinion gear sets to be modeled.

Friction, back-lash, and manufacturing inaccuracies in tooth profiles are not modeled.

## Format

<Constraint_Gear
id             =   "integer"
[ label          =   "string" ]
joint1_id      =   "integer"
joint2_id      =   "integer"
cv_marker_id   =   "integer"
[ is_virtual     =  {"FALSE" | "TRUE"} ]
</Constraint_Gear>

## Attributes

id
Element identification number (integer>0). This number is unique among all Constraint_Gear elements.
label
The name of the Constraint_Gear element.
joint1_id
Specifies the first Constraint_Joint whose output is coupled by the gear constraint.
The parameter is mandatory. The joint type must be one of the following:
• Revolute
• Translational
• Cylindrical
joint2_id
Specifies the second Constraint_Joint whose output is coupled by the gear constraint. The parameter is mandatory. The joint type must be one of the following:
• Revolute
• Translational
• Cylindrical
cv_marker_id
Specifies a Reference_Marker whose origin defines the contact point. Its z-axis defines the direction of motion at the contact point. The parameter is mandatory. cv_marker_id must belong to the body containing the housing.
is_virtual
Defines whether the constraint is virtual or regular. If is_virtual is set to TRUE, the constraint is implemented as a virtual constraint. If is_virtual is set to FALSE, the constraint is implemented as a regular, algebraic constraint. This parameter is optional. The default is FALSE. See Comment 22 in Constraint: Joint for more information about virtual joints.

## Example

The image below shows a spur gear pair.

Spur gear 1, with a pitch radius R1, is connected to the housing (shown as a red box) with Revolute Joint 1. It rotates about a fixed axis $\stackrel{\to }{\alpha }$ . Spur gear 2, with a pitch radius R2, is also connected to the housing with Revolute Joint 2 and it rotates about a fixed axis $\stackrel{\to }{b}$ . Both axes are coming out of the plane of the paper.

The contact point between the two gears, shown as a red dot in the image above, is fixed with respect to the housing. It is defined by a Reference_Marker CV. The origin of CV defines the contact point and thus the velocity ratio of the gear set. The z-axis of CV points to the direction of motion at the contact point and therefore the direction of the contact forces at the teeth.

If the ID of the cv_marker, CV, is 1101. The Constraint_Gear object may be defined as:

<Constraint_Gear
id            = "1"
joint1_id     = "1"
joint2_id     = "2"
cv_marker_id  = "1101" >
</Constraint_Gear>