Experimental measurement of the bearing characteristics of straight-line flexure mechanisms

In this paper, we present an experimental set-up and procedure to accurately measure the bearing characteristics of any single Degree of Freedom (DoF) straight-line flexure mechanism. Bearing characteristics include stiffness in the bearing and motion directions, and error motions in the bearing directions. In particular, we present this characterization for the traditional paired double parallelogram (DP-DP) flexure and its recently-reported improved variation, the clamped paired double parallelogram (C-DP-DP) flexure. Of particular interest is the bearing direction stiffness and its variation with motion direction displacement. While the bearing stiffness for both mechanisms has been extensively predicted via analysis and its consequences have been observed in experiments, its direct measurement poses several challenges and is not found in the literature. This paper presents an experimental set-up that is reconfigurable to accommodate both the above two flexures, comprises a novel virtual pulley concept, and employs carefully selected ground mounting and sensor locations, among other features that enable the desired measurements. The experimental results agree well with analytical predictions and generate insight into the importance of ground mounting, finite compliance of mechanism features that are generally assumed to be rigid, and manufacturing tolerances.