17.1 BASICS

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When we deal with geometries in two dimensions we have three position variables (dof) for each rigid body (two for position, one for orientation).

When a problem is expanded to three dimensions we then have six position variables (dof) for a rigid body (three for position, and three for orientation).

These added degrees of freedom expand the complexity of the problem solutions. There are a few potential approaches,

- look for regularities that simplify the problem (scalar)

- vector based approaches (positions)

- matrix based approaches (positions and orientations)

Consider the example of the spherical joint - all of the axes of rotation coincide.

17.1.1 Degrees of Freedom

The scalar and vector approaches are easily extended to 3D problems. One significant difference is that the polar notations are no longer available for use.

We can determine the number of degrees of freedom using a simple relationship that is an extension of the Kutzbach criteria,

Consider the number of degrees of freedom in the linkage below,