Kinematics of robot manipulators via line transformations

Robot kinematics is an extensively researched subject and several well developed techniques for the analysis of robot manipulators and spatial mechanisms exist. Most of these methods are based on point transformations. However, far less research is in evidence for line transformations. Lines and screws are more fundamental to velocity analysis and hence line transformations are believed to be better suited for the kinematic and static analysis of manipulators. In this article, the kinematics for serial chain manipulators using line transformations is investigated. Dual number quaternions are used as spatial transformation operators since they allow compact representation of both rotations and translations. Further, the symbolic computation of the direct and inverse kinematics equations using dual number quaternions is described.