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 which show its performance on the double butterfly linkage and on larger linkages formed by the concatenation of basic patterns.

This paper presents an interval propagation algorithm for variables in planar single-loop linkages. Given intervals of allowed values for all variables, the algorithm provides, for every variable, the whole set of values, without overestimation, for which the linkage can actually be assembled. We show further how this algorithm can be integrated in a branch-and-prune search scheme, in order to solve the position analysis of general planar multi-loop linkages. Experimental results are included, comparing the method's performance with that of previous techniques given for the same task.

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Abstract-This paper presents a numerical method able to compute all possible configurations of a planar linkage. The procedure is applicable to rigid linkages (i.e., those that can only adopt a finite number of isolated configurations) and to mobile ones (i.e., those that have internal degrees of freedom). The method is based on the fact that this analysis always reduces 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, geometric in nature, and easy to implement, yet it provides solutions of the desired accuracy in short computation times. Experiments are included which show its performance on the double butterfly linkage, for which an accurate an complete discretization of its configuration space is obtained.

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