A Geometrical Approach to the Inverse Kinematics of 6R Serial Robots With Offset Wrists

The computation of the joint-angle values of a 6R serial manipulator for a given end-effector pose is more difficult for architectures lacking the conventional spherical wrist. Despite this added complexity, such arms have increasingly gained acceptance as they provide better dexterity for a number of tasks. The paper presents a geometric-analysis method for the inverse kinematics of a robot with an offset wrist. The sought postures are shown to correspond to the roots of four separate univariate trigonometric equations for the sixth joint angle. A standard numerical solver is applied to derive all sets of possible real solutions. By back-substitution, all the remaining angular variables are found in succession. Two particular arm designs are considered and full sets of solutions are obtained by the discussed approach. The method is easy to implement and can be applied to various 6R serial robots.