The well-known finite-position planar theory of kinematic synthesis (the so-called Burmester theory) and the corresponding spherical theory are derived from the results of the general spatial theory which has been given in a companion paper [1]. Other special displacements studied are those for which the author has coined the names “similarity transformation,” “pseudoplanar,” and “pseudospherical.” These results, as well as those obtained in [1], are shown to be applicated to the synthesis of spatial, spherical, and planar linkages. Several numerical examples are presented.

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