Using the concept of kinematic mappings, a theorem is derived which relates the order and circularity of a rational algebraic planar motion to the order and cirularity of the rotation curve and the order of a rotation function (which depends only on the relative orientation of the fixed and moving planes). It is shown that the equations of the point-paths, centrodes and directrices follow from the image space and its mappings in a straightforward fashion. Several examples are presented showing how to qualitatively synthesize whole cycle motions.

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