In this paper we derive an analytic method for obtaining infinitesimal kinematic synthesis results as a limiting process from finitely separated position kinematics. New relationships are introduced and a new numerical method is presented. Within the scope of linear, analytic theories, the loci associated with infinitesimal position theory and the loci associated with hybrid finite-infinitesimal position theory are shown to always be limiting cases of the corresponding finite theory. These new methods serve to unify finite, infinitesimal, and hybrid kinematic synthesis theories.

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