An Analytical Approach for Calculating the First Natural Frequency of Flexure Hinges with Variable Cross-Sections for Compliant Mechanisms

In this paper, we present an analytical approach for enabling the calculation of the natural frequencies of flexure hinge contours with variable cross-sections. In regard to the planned implementation of this approach into an existing analytical method based on Euler-Bernoulli-beams and the transfer matrix method, the flexure hinges will be discretized into a specific amount of individual beam segments with constant cross-sections. Three possible discretization approaches are presented, the optimum numbers of segments is found and the influence of the mass on the actual natural frequency calculation is discussed. The analytical method is finally validated on a compliant parallel four-bar linkage. The studies show that the presented approaches yield sufficiently accurate results for the calculation of the natural frequencies of compliant mechanisms with flexure hinges with variable cross-sections.