The measurement of kinematic accuracy for various configurations of parallel manipulators

The kinematic equation of a general Stewart-Gough platform is formulated and the error mapping model is derived. The relationships between input and output errors of both a single kinematic link and the whole manipulator are presented and analyzed. The singular values of a Jacobian matrix are used to define three error sensitivity measures, namely the comprehensive error sensitivity, the absolute error sensitivity and the directional error sensitivity. According to these measures, two indicators, the comprehensive error coefficient and the comprehensive error degree, are defined to evaluate the kinematic accuracy for various configurations of this type of mechanism. Based on the structure of a real parallel kinematic machine tool, several kinematic accuracy evaluation experiments are depicted graphically. The study shows that the evaluation measures proposed in this paper are very useful to help designers and operators correctly choose the manipulator configurations for obtaining the high kinematic accuracy.