Kinematic error bound analysis of the Stewart platform

In recent robotics research, the Stewart platform has been increasingly studied for possible use as a machine tool in view of the advantages of high stiffness and accuracy over serial-type manipulators. In designing and controlling a machine tool, accuracy is one of the most important factors to be considered. This article presents the development of methods of the forward and inverse error bound analyses of the Stewart platform. The forward error bound analysis is used to find the error bound of the end-effector when the error bounds of the joints are given, while the inverse error bound analysis is used to determine those of the joints for the given error bound of the end-effector. The inverse error bound analysis is important since it provides a designer with a way to determine the tolerance limits of the joints. Based on the kinematic error model we propose, two eigenvalue problems corresponding to the forward and inverse error bound analyses are derived. The relationship between the eigenvalues and error bounds is explained. It is shown that the eigenvalue problems are consistent with a change of unit, and most importantly, that the eigenvalues from the forward and inverse error bound analyses are reciprocal to each other.