Type synthesis of analytic translational parallel manipulators

An analytic parallel manipulator is a parallel manipulator for which a characteristic univariate polynomial of degree four or lower can be obtained symbolically. This paper presents a geometric approach to the type synthesis of analytic TPMs (3-legged 3-DOF translational parallel manipulators). Leg-surfaces of a TPM are introduced and a geometric interpretation of the forward displacement analysis of a TPM is given. A geometric approach to the type synthesis of analytic TPMs is then proposed. Finally, a broad class of analytic TPMs is obtained.