Abstract
Abstract The displacement analysis problem for planar mechanisms can be written as a system of algebraic equations, in particular as a system of multivariate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods which have been used to solve this problem. This paper explores an alternate approach, based on Gröbner bases, to solve the displacement analysis problem for planar mechanisms. It is shown that the reduced set of generators obtained using the Buchberger’s algorithm for Gröbner bases not only yields the input-output polynomial for the mechanism, but also provides comprehensive information on the number of closures and the relationships between various links of the mechanism. Numerical examples illustrating the applicability of Gröbner bases to displacement analysis of 10 and 12-link mechanisms and determination of coupler curve equation for 8-link mechanisms are presented.
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