A new algebraic method for inverse kinematics(II)

In the preceding article, the algebraic structure of Lie algebra D is presented, a new method of decomposition a general displacement into a product of three other displacements is introduced using the general Olinde-Rodrigues formula[1]. The aim of this paper is to obtain the kinematic solution of a system R = RthetaRphiRpsi, that is to say, the equivalent displacement R, described by its generator xi, rotation theta and translation d, when three displacements RthetaR,R-phi(psi), are given. In order to simplify the calculations, dual quaternion conception is introduced. These results can be used to analyze different configurations for a complex mechanism. At the end, an example of manipulator arm of change cutting tool XHK5140 is presented[5].