Inverse kinematic formula for a new class of 6R robotic arms with simple constraints

A systematic and unified kinematic modelling method for a new class of 6R robotic arms is investigated, which separates the coupled joint variables without raising degrees. To begin, successive products of the tangent-form DCMs and quaternions yield the non-redundant kinematic equations. By providing the derived position vectors, new inverse kinematic formulas are then invented for general 6R robotic arms. Based on this, a degree-reduced condition is found out to ideally reduce the kinematic formulas of five coupling variables to three while the degrees remain constant, which benefits for a light computational resource. A new class of robotic arms satisfying the degree-reduced condition is proposed, including simple kinematic constraints of two adjacent parallel or orthogonal. The inverse kinematic software testing proves the efficiency of the method: the running time is less than 2 milliseconds; the relative position and orientation variations are less than 10-11. This study can be taken as a theoretical basis for the inverse kinematic research of 6R robotic arms, which provides a brand-new way to establish the kinematic formulas and exhibits a relatively simple kinematic structure for precise industrial use. Moreover, the proposed method is expected to be used to reduce the degrees of kinematic modelling polynomials of higher-DOF robotic arms.