A generalized treatment for combinations of infinitesimally and finitely separated coplanar positions is presented for four, five, and six positions lying symmetrically about an axis in the reference plane. Symmetry of the first and second kind are shown to be distinct because of the constraint system and not due to the form of the motion specification. The solution for the Burmester points is represented by the intersection of the Bottema conics. This development is supported by an algorithm for synthesizing five multiply separated positions in coplanar motion.

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