Exact interval propagation for the efficient solution of position analysis problems on planar linkages

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.

► Solution ranges for variables in planar linkages are computed from link lengths. ► Exact ranges for variables that are compatible with a constrained one are obtained. ► A multiple interval propagation algorithm deals with constraints on several variables. ► Arbitrary multi-loop linkages can be solved with a branch-and-prune process.