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# Distance Constraint

Constraint that maintains a fixed distance between the origins of two frames

Constraints

## Description

This block represents a fixed distance between the origins of the base and follower frames. This constraint allows the base and follower frames to translate and rotate with respect to each other, with the requirement that their origins maintain the distance that you specify. Use this constraint in conjunction with other joint blocks.

## Dialog Box and Parameters

The dialog box contains one active area, Properties.

Distance

Positive real number specifying the distance between the origins of the base and follower port frames. The default value is 0.

## Constraint Distance

Using the Distance Constraint block, you can fix the distance between the origins of the Base and Follower port frames. Extending the Pythagorean theorem to 3–D space gives the distance between the two port frame origins:

In agreement with the definition, any two sets of (X1-X0, Y1-Y0, Z1-Z0) parameters yielding the same d value represent the same constraint distance. For example, the sets (L, 0, 0), (L/sqrt(2), L/sqrt(2), 0), and (L/sqrt(3), L/sqrt(3), L/sqrt(3)) represent the constraint distance L.

It is possible to constrain the distance between the two port frame origins while varying the (X, Y, Z) coordinates of the Follower port frame with reference to the Base port frame. The set of all possible translations consistent with the constraint distance describes a spherical surface whose center coincides with the origin of the Base port frame. Model topology, as well as joints and other kinematic constraints, can act to reduce the set of allowed translations between the two constrained port frames.

## Degrees of Freedom Between Constrained Frames

The Distance Constraint block eliminates a single translational degree of freedom. In the absence of joints and other constraints in the kinematic loop, the two port frames retain two translational and three rotational degrees of freedom with respect to each other. The large number of degrees of freedom can produce unexpected assembly and simulation results when the Distance Constraint block is used as the sole kinematic constraint in a model. You can further constrain port frames by adding Joint and Constraint blocks to the kinematic loop.

## Constraint Consistency Requirement

The distance constraint must not conflict with joints and other constraints present in the same kinematic loop. For example, any distance constraint which violates the requirement that the origins of the two port frames of a Revolute Joint block remain coincident at all times results in assembly and simulation errors.

## Ports

The block contains frame ports B and F, representing base and follower frames, respectively.