# Mechanisms and Robot Kinematics: Algebraic Foundations

Saturday, September 16, 2006 - 9:00am - 9:50am

EE/CS 3-180

Charles Wampler (General Motors Corporation)

This talk will discuss how many of the basic questions in mechanism

science are naturally formulated as systems of polynomial equations.

These questions include both analysis problems (how does this

mechanism move?) and synthesis problems (which mechanisms will move

the way I require?). Once such a problem has been formulated as a

system polynomials, the irreducible decomposition of the solution set

of the system becomes a powerful tool for describing the answer. We

will discuss how some questions can be approached in stages by

computing irreducible decompositions of subsets of the original

equations and then intersecting solution components. Finally, we will

see how some questions about the existence of special mechanisms are

nicely formulated as fiber products of algebraic sets.

science are naturally formulated as systems of polynomial equations.

These questions include both analysis problems (how does this

mechanism move?) and synthesis problems (which mechanisms will move

the way I require?). Once such a problem has been formulated as a

system polynomials, the irreducible decomposition of the solution set

of the system becomes a powerful tool for describing the answer. We

will discuss how some questions can be approached in stages by

computing irreducible decompositions of subsets of the original

equations and then intersecting solution components. Finally, we will

see how some questions about the existence of special mechanisms are

nicely formulated as fiber products of algebraic sets.

MSC Code:

70B15