A kinematic theory is developed involving infinitesimally close coplanar positions of a moving plane, based on a finite cycloidal kinematic theory of plane motion, which was shown to include Burmester’s classical centerpoint-circlepoint theory as one of several special cases. The infinitesimal theory is developed for both the general cycloidal and for the special circular (Burmester) cases. Applications are derived for closed-form analytic synthesis of higher-order approximate path and motion generator linkages. Examples are given, and implementations of the theory in the form of computer programs are made available.

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