Approximative approach of forward-kinematics for one-link manipulator using belt-formed pulleys

The control of joint stiffness of a robot is extremely important to guarantee safe and dexterous motion, especially for the collaborative operation between a human and a robot. Some devices to vary joint stiffness have been proposed for a tendon-manipulator so far. However, the previous devices have problems such as a complex structure, increase of friction, increase of inertia and so on. In order to overcome these problems, we proposed a belt-formed pulley to vary the joint stiffness. Inserting belt-formed pulleys into routes of wires, the joint stiffness of a tendon-driven robot can be varied depending on internal force among wires. The system using belt-formed pulleys has many advantages such as a simple structure, low friction, lightness in weight and low cost. However, little is known about kinematic issues of the tendon-manipulator using belt-formed pulleys. In this paper, we propose a numerical solving method of forward kinematics (to obtain joint angles from wire length) using an approximate model of a belt-formed pulley. In addition, we expand this solving method into numerically calculation of the joint stiffness from given wire length. First, we present the numerical solving method of forward kinematics for a 1-DOF manipulator. Secondly, the usefulness of the proposed method is demonstrated through experimental result. Lastly, we propose numerically calculation of the joint stiffness and also investigate the accuracy of this method through experimental result.