Exact solution of inverse kinematic problem of 6R serial manipulators using Clifford Algenbra : applications of Clifford Algebra in robotics

The inverse kinematic problem of 6R serial manipulators has been the focus of many researchers for several decades now. The main interest has been in inverse kinematics of 6R serial manipulators with arbitrary geometry. This problem has been always an obstacle in designing industrial robots, as they had to be de­ signed in such a simple way to avoid complication of solving this problem. Solving the Inverse Kinematic Problem is about finding a set of six angles of rotations that correspond to a given pose of the end effector (gripper). One of the major difficulties in solving this problem was obtaining an exact solution in a simple form ; which is very important for speeding up the process of calculation and minimizing the calculations errors that can easily occur in algebraic solutions. Many solutions have been suggested for this problem varying between numerical, algebraic or geometric solutions. It has been previously shown that the joints of a general 6R manipulator can orient themselves in 16 different configurations for a given pose of end effector. However, there are no good practical solutions available that give a level of performance expected of industrial manipulators. In this work, Clifford Algebra was used to model the Inverse Kinematic Prob lem of 6R serial manipulators and an algorithm has been developed to solve this problem by setting one angle to be free and finding the other angles in terms of this free angle. Based on this solution, there exist an infinite number of solutions for a union of intervals of the free angle.