Analysis of Errors in Precision for Closed Loop Mechanisms

An algorithm to analyze the relations of error components for closed loop mechanisms is introduced. The error components considered are errors in link dimensions and error motions due to joint clearances. In order to completely characterize the physical shape of a link, first a revision of the Denavit-Hartenberg symbolic notation is introduced. Then, an error matrix is proposed to account for the effects of error motions due to joint clearances. Six independent equations are obtained. The major benefit from these equations is the capability of assessing the influence of each error component on a machine’s accuracy. This analysis is particularly useful to allocate a machine’s tolerances at its design stage and to characterize the performance of an existing machine.