# Degrees of Freedom

An unconstrained rigid body in space has six degrees of freedom: three translational and three rotational. It can move along its X, Y, and Z axes and rotate about its X, Y, and Z axes.

When you add a constraint, such as a concentric mate, between two rigid bodies, you remove degrees of freedom between the bodies. The two bodies remain constrained, positioned with respect to one another regardless of any motion or force in the mechanism. You can use mates to constrain motion by removing various degrees of freedom.

For example, a concentric mate removes two translational degrees of freedom and two rotational degrees of freedom between two rigid bodies. Adding a distance or coincident mate to the faces removes the final translational degree of freedom.

If each rigid body has a point on the joint on the center line of the concentric mate, those two points remain the same distance apart. They can rotate only with respect to one another about one axis, the center line of the concentric mate. This combination of mates produces a single-degree-of-freedom joint, because it allows a single rotation between the rigid bodies.

When you use a Motion Analysis study to calculate motion, it calculates the number of degrees of freedom in your mechanism and removes redundant mates as it determines and solves the equations of motion for your assembly.

When a mechanism has a closed loop, such as a four-bar linkage, there can be redundant mates. There are three redundant mates in a four-bar linkage when all of the mates are concentric. This is because each side of the loop (starting from ground) constrains the connecting rod to stay in the plane of the assembly.

The software attempts to resolve constraints imposed by the redundant mates automatically, and can do so easily for a four-bar linkage.

## Checking Degrees of Freedom and Redundancies

For Motion Analysis type studies, you can calculate the number of degrees of freedom in a model as well as the redundancies introduced by mates.

1. Click Calculate (MotionManager toolbar).
2. Right-click Mates (MotionManager tree) and click Degrees of Freedom.
The Degrees of Freedom dialog box provides the degrees of freedom in the model and a list of the redundant constraining mates.
Redundant constraints can provide inaccurate motion calculations. To address this problem, try one or more of the following, in order, as appropriate for your model:
1. Create rigid subassemblies and rigid groups for components that are fixed with respect to the assembly motion.
2. Replace redundant mate pairs that form a hinge with hinge mates.
3. Replace redundant mates with mate primitives.
4. Replace mates with bushings.