Computation of the effects of link deflections and joint compliance on robot positioning

Actual trajectories of robot manipulators usually differ from the planned trajectories partially because of the effects of link deflections and joint compliance. This paper presents an efficient computation scheme to calculate the actual positions and orientations of the end-effectors of manipulators consisting of straight thin-walled hollow links and revolute joints, of which most contemporary robots are made up. Local principal coordinate frames are defined for deflection analysis. Displacements are computed using formulae derived from classical beam theory. For compliance analysis, the robot joints are considered as torsional springs, where the first order approximation is applied. A hypothetical two-link robot is used to demonstrate the techniques. Results are verified by analytical solutions, and the differences are less than 1% of the deflections.