# Elimination Methods for the Types of Equations that Arise in the
Algebraic Geometry of Rigid Body Transformations

### Bernard Roth

Mechanical Engineering Department

**Stanford University**

### Abstract

This talk will review the common methods of obtaining equations for the analysis and
design of systems of rigid bodies which have relative motions. The algebraic and the
essential sine-cosine character of such equations is pointed out. Once this is
established, the main body of the talk will deal with the solution of sets of such
equations. Emphasis will be placed on elimination methods, and especially on methods of
obtaining auxiliary equations from the original set.

This talk will review what we have learned in the last several years by the use of
elimination methods. It will be pointed out that classical techniques of elimination
usually are too cumbersome, but with slight modifications the same basic concepts can lead
to effective algorithms.

Bernie Roth is a Professor on the faculty of the Design Division of the Mechanical
Engineering Department at Stanford University.

Edited by Leonidas Guibas