Quaternion Based Force-Torque Analysis of Open Serial Kinematic Structures

Force-torque analysis of open serial kinematic structures is considered in this work. The close relation between vector and pure quaternion representation of force and torque balance equalities is presented together with the quaternion position and orientation representation of links. These equalities embody the common starting point of the relevant problems concerned with the static analysis. One task is to establish prismatic joint forces and revolute joint torques caused by an external endpoint force, torque, and the gravity of links in the given endpoint position and orientation. Since the inverse kinematics is involved in this problem, redundant structures admit additional restrictions in the form of the cost function depending on joint variables. Another task is to establish the external force and torque, having measured forces in prismatic and torques in revolute joints in the given position of joints. The aim of the paper is to present the common base of the vector force-torque balance equalities and the quaternion representation of positions and orientations of any open multiple link redundant or nonredundant serial kinematic structure.