Design Space Analysis of Distributed Compliance in Segmented Beam Templates of Compliant Mechanisms

Abstract

A significant amount of research has been conducted in developing optimal synthesis techniques for compliant mechanisms with the expectation that distributed devices would result from the continuum design domain. However, it is commonly noted that much of this work has resulted in mechanisms that show localized rather than distributed compliance. This behavior has been attributed to a variety of sources including numerical discrepancies in the model, objective function formulation, and design parameterizations. In this paper, the nature of compliance distribution over particular objective function formulations and design parameterization are further considered in the absence of numerical or resolution issues. The intent is to better understand the behavior of the objective function over multidimensional subsets of the design space that include a direct measure for distribution of compliance. The approach is based on a simple, representative compliant mechanism formed as a segmented beam model. This mechanism is considered to be representative of compliant mechanism behavior in systems where elastic deformation is dominated by bending. Closed-form solutions for the elastic response of this representative mechanism are presented and parametric studies of the response of traditional objectives over subsets of the design space are conducted. The results show that in the absence of numeric artifacts, mechanism efficiencies are improved as mechanisms tend toward lumped compliance when single objectives are considered on mechanisms dominated by bending. However, when more than one objective is deemed important in the design, there exist preferred regions of the workspace, not necessarily in a lumped region, that depend largely on the interaction of the multiple objectives. Of these preferred regions, one lies in a moderately lumped region (h2/h1 ≈ 0.2) and one in a distributed region (h2/h1 ≈ 0.7). The designs in these regions reveal a higher viability in simultaneously satisfying the multiple objectives. This result is based on a visualization of the design space based on measuring the correlation of a multiple objectives over the design space. The results demonstrate several of the factors which contribute to this behavior, and provide an initial measure of the importance of each. Finally, suggestions are provided based on these results that can be used to improve the optimization process if the desire is to achieve distributed compliance.