# Documentation

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# Parallel Constraint

Constant parallel relationship between two body axis vectors

## Library

First Generation/Constraints & Drivers

## Description

The two Bodies connected by a Parallel Constraint are restricted in their relative rotational motion. The Parallel Constraint is connected on either side to a Body CS, one on each Body. A vector aB defined in one Body CS on the base body remains parallel to a second vector aF defined in another Body CS on the follower body.

The Parallel Constraint block requires that:

`$|{a}_{B}\cdot {a}_{F}|/\left(|{a}_{B}||{a}_{F}|\right)=1$`

You specify the initial direction to which both vectors must remain 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.

Parallel Constraint is assembled: the Body CS origin on the base body must be initially collocated with the Body CS origin on the follower body, to within assembly tolerance.

You can connect a Constraint & Driver Sensor to any 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 Parallel 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, Parallel Constraint Base and Follower Body Connector Ports.

Current follower

When you connect the follower (F) connector port on the Parallel 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, Parallel 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`.

Parallel Constraint Base and Follower Body Connector Ports

## Parameters

Parallel Constraint Axis [x y z]

Enter the axis vector defining the initial direction of the two body axis vectors ab, af. These body axis vectors are restricted to always remain parallel to this initial axis. The default is `[1 0 0]`.

Reference CS

Using the pull-down menu, choose the coordinate system (World, the base Body CS, or the follower Body CS) whose coordinate axes the initial Parallel constraint axis is oriented with respect to. This CS also determines the absolute meaning of reaction forces/torques at this Constraint. The default is `World`.

See Constraining and Driving Degrees of Freedom for more on restricting DoFs with Constraints.

See Checking Model Topology and How Simscape Multibody Software Works for more on using constraints in closed loops.