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This paper investigates the conditions in the design parameter space for theexistence and distribution of the cusp locus for planar parallel manipulators.Cusp points make possible non-singular assembly-mode changing motion, whichincreases the maximum singularity-free workspace. An accurate algorithm for thedetermination is proposed amending some imprecisions done by previous existingalgorithms. This is combined with methods of Cylindric Algebraic Decomposition,Gr\"obner bases and Discriminant Varieties in order to partition the parameterspace into cells with constant number of cusp points. These algorithms willallow us to classify a family of degenerate 3-RPR manipulators.

Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators