New Algorithm For Inverse Kinematics Of 6 DOF Serial Manipulator

Faced too many types of serial spatial robot mechanical, a universal method to solve inverse kinematics analysis about them attracted many researchers of the kinematics community and become their research goal. In this paper we refer to traditional solutions of the inverse kinematics of a serial mechanisms, double quaternions is introduced firstly to inverse kinematics analysis of 6 DOF serial manipulator and try to develop a new universal algorithm for inverse solution of all kinds of 6 DOF serial manipulator based on double quaternions and some valuable results are obtained.In this paper we introduce the mathematical and geometrical tools, we recall the notations about quaternion, dual quaternions and double quaternions to describe serial chains and discuss the method of Dixon elimination that we used in this paper. The rotation and translation of coordinate systems in double quaternions are deduced based on the transform between double quaternions and dual quaternion. The kinematics equations of serial robot are constructed in terms of double quaternions.Variable are separated from the equation of the double quaternions, novel inverse solution algorithm of a general 6R serial manipulators is obtained via linear algebra and Dixon resultant formulation, and this algorithm also can be applicable to the inverse kinematics analysis of the robots with 16 roots, such as 1P5R and 4R1C, so it has universal usage.This method is applied to solve the inverse kinematics analysis of the special-dimension which is regarded as general 6R robots via adjusting some dimensions a little under the precision permitted. Then two examples of a painting robot and PUMA560 robot are given to prove it.Finally a new universal inverse solution algorithm for group 1 mechanisms with two roots is developed, based on a group kinematics equation of angle is added. Then take RRPPC and RCPC robots for two examples to prove this algorithm.