Synthesis of C⁰ Path-Generating Contact-Aided Compliant Mechanisms Using the Material Mask Overlay Method

Contact-aided compliant mechanisms (CCMs) are synthesized via the material mask overlay strategy (MMOS) to trace desired nonsmooth paths. MMOS employs hexagonal cells to discretize the design region and engages negative circular masks to designate material states. To synthesize CCMs, the modified MMOS presented herein involves systematic mutation of five mask parameters through a hill climber search to evolve not only the continuum topology but also to position the rigid, interacting surfaces within some masks. To facilitate analysis with contact, boundary smoothing is performed by shifting boundary nodes of the evolving continuum. Various geometric singularities are subdued via hexagonal cells, and the V-notches at the continuum boundaries are alleviated. Numerous hexagonal cells get morphed into concave subregions as a consequence. Large deformation finite-element formulation with mean-value coordinates based shape functions is used to cater to the generic hexagonal shapes. Contact analysis is accomplished via the Newton–Raphson (NR) iteration with load incrementing in conjunction with the augmented Lagrange multiplier method and active set constraints. An objective function based on Fourier shape descriptors (FSDs) is minimized subject to suitable design constraints. Two examples of path-generating CCMs are presented, their performance compared with a commercial software and fabricated to establish the efficacy of the proposed synthesis method.