Model Element

Description

Constraint_Gear defines a gear constraint between two bodies.

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" >

</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:

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:

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.

Comments

cv_marker definition for a rack-and-pinion gear set

cv_marker definition for a worm and worm-wheel gear set

Example

The image below shows a spur gear pair.

Defining a spur-gear set using CONSTRAINT_GEAR

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 .  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 .  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>

Model Element

Description

GEAR defines a gear constraint between two bodies.  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.

Declaration

def GEAR(id, LABEL="", JOINTS=[0, 0], CV=0):

Attributes

id

Element identification number (integer>0).  This number is unique among all the GEAR elements.

LABEL

The name of the GEAR element.

JOINTS

Specifies the ID of two joints whose output is coupled by the gear constraint. The parameter is mandatory.  The joint type must be one of the following:

CV

Specifies the ID of the marker whose origin defines the contact point.  Its z-axis defines the direction of motion at the contact point.  The parameter is mandatory.  CV must belong to the body containing the housing.

Comments

See Constraint_Gear

Example

The example below shows how a gear may be defined>

GEAR(1, LABEL="Gear 0", JOINTS=[1,2], CV=1101)