Box approximations of planar linkage configuration spaces

Abstract

This paper presents a numerical method able to compute all possible configurations of planar linkages. The procedure is applicable to rigid linkages (i.e., those that can only adopt a finite number of configurations) and to mobile ones (i.e., those that exhibit a continuum of possible configurations). The method is based on the fact that this problem can be reduced to finding the roots of a polynomial system of linear, quadratic, and hyperbolic equations, which is here tackled with a new strategy exploiting its structure. The method is conceptually simple and easy to implement, yet it provides solutions of the desired accuracy in short computation times. Experiments are included that show its performance on the double butterfly linkage and on larger linkages formed by the concatenation of basic patterns.