Error analysis of parallel manipulators based on differential operators

A method for the error analysis of parallel manipulators based on differential operators is presented in this paper, in order to design parallel manipulators and relevant engineering products with high accuracy (such as parallel machine tools, packaging machinery). For the given errors including all the structural dimensions, the pose errors of the end effectors can be derived by a forward kinematics solution. After altering in turn one of the errors of structural parameters, the pose errors relevant to the given errors can be calculated. Those parameters sensitive to the end effector errors can be found. Relations between errors of the pose and structural types have been discussed through numerical examples (two different types of Stewart platforms). Compared with Stewart platform, double triangular platform manipulators have higher stability. In this way, design accuracy of structure parameters might be reasonably determined in numerical quantities.