A spherical parallel manipulator (SPM) refers to a 3-DOF parallel manipulator in which the moving platform has only three pure rotational degrees of freedom of motion relative to the base. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the input validity check of SPMs are dealt with in sequence. SPKCs with and without inactive joints are synthesized. The number of over-constraints of each SPKC is also given. The phenomenon of dependent joint groups in a SPKC is revealed for the first time. The input validity check of SPMs is also simplified.

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