19 . Kinematics of Robot Manipulators in the Motor Algebra ∗

In the literature we find a variety of mathematical approaches for solving problems in robotics which we will review now briefly. Denavit and Hartenberg [60] introduced the mostly used kinematic notation for lower pair mechanisms based on matrix algebra, Walker [243] used the epsilon algebra for the treatment of the manipulator kinematics, Gu and Luh [99] utilized dual– matrices for computing the Jacobians useful for kinematics and robot dynamics and Pennock and Yang [188] derived closed–form solutions for the inverse kinematics problem for various types of robot manipulators employing dual–matrices. McCarthy [171] used the dual form of the Jacobian for the analysis of multi–links similarly. Funda and Paul [87] gave a detailed computational analysis of the use of screw transformations in robotics. These authors explained that since the dual quaternion can represent the rotation and translation transformations simultaneously it is more effective than the unit quaternion formalism for dealing with the kinematics of robot chains. Kim and Kumar [132] computed a closed–form solution of the inverse kinematics of a 6 degree of freedom robot manipulator in terms of line transformations using dual quaternions. Aspragathos and Dimitros [9] confirmed once again