The kinematics of spatial robotic bevel-gear trains

A systematic approach is developed for the kinematic analysis of multi-degree-of-freedom robotic bevel-gear trains. The approach is based on the idea that the motion of a bevel-gear-type and effector can be described by an equivalent open-loop chain and that the relative rotation between every two adjacent links in the equivalent open-loop chain can be derived from a set of fundamental circuit equations and coaxial conditions. The theory is demonstrated by the kinematic analysis of two robotic wrists