A new approach to error analysis in parallel kinematic structures
In this paper, a method is proposed to describe the displacements of the TCP (tool center point) in terms of error amplifications for uncertainties in all kinematic parameters using the differential geometric properties of kinetostatic transmission. The error amplifications can be calculated from the internal forces in the mechanism, when we apply unity wrenches to the TCP. The proposed force based method delivers insight in the impacts of geometrical errors in serial and parallel mechanisms and provides an efficient way to calculate the error amplifi-cation coefficients. An example demonstrates that the algorithm is suitable for serial and for parallel mechanisms as well. The algorithm is capable to find the parameters that affect the precision as well as to quantify the influence of these parameters on the accuracy of the end-effector. For the typical dimension of errors that arise from manufacturing and assembly the proposed method is exact. The examples show that the force based method needs less time to rate all parameters than the other approaches need to calculate the error amplification matrix for a preselected set of parameters. The overall error amplification of the Linapod varies only slightly in the workspace and demonstrates that steps like calibration are needed in addition to manufacturing tolerances to ensure a feasible accuracy for machine tools.
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