Solution of the inverse kinematic problem of a robot manipulator with eulerian joints

Abstract Solved in this paper is the inverse kinematic problem for a six-degree-of-freedom robot manipulator with eulerian joints. Every joint consists of a couple of hinges whose axis are angularly positioned at 90° between each other, and each tilted at 45° relatively to the arm axis. An offset is present between every couple of hinges forming the joint. The kinematics of such a manipulator can be easily studied if an equivalent rotation point is found so that the offset vanishes. The original kinematics chain is then reduced to a simpler one: a backbone formed by three links and three quasi- sphcrical hinges. Geometrical considerations lead to find the six joint variables given the position and orientation of the backbone end with respect to the reference coordinate system. A further transformation is needed to relate the backbone end to the manipulator end effector. The solution is obtained in closed-form. A standard joint employing such a kinematics has been built in the Mechanical Department of the Politecnico di Torino. The procedure is illustrated with the analysis of a modular robot manipulator having three such joints.