Topological Analysis of Tendon-Driven Manipulators

Abstract

This paper investigates the effect of tendon routing on kinematic and static force transmission associated with tendon-driven manipulators. The transmission characteristics can be described by the velocity and/or force ellipsoid. We have shown that the effect of tendon routing can be characterized by a condition number and the direction of a homogeneous solution. The condition number is defined as the ratio of the maximum to the minimum singular value of the structure matrix and the homogeneous solution is the set of tendon forces that results in no net joint torques. A methodology for calculating maximum tensions in a tendon-driven manipulator has been developed. We have also shown that among the various tendon routings in three- DOF manipulators, the one with an isotropic transmission ellipsoid possesses minimal maximum tendon force.