INTERACTIVE SHAPE DESIGN OF COMPLIANT MECHANISMS USING GRAPHIC STATICS

Abstract

We present a method to design the shape of a compliant mechanism to obtain large displacement at the output point in the desired direction while making the displacement in the orthogonal direction nearly zero. As the nonlinear constraint of the orthogonal displacement is challenging in gradient-based optimization, we adapt an interactive graphic statics method, which has been used so far to design only stiff trusses. We justify the use of truss models for compliant mechanism design because optimal topologies and shapes tend to be similar regardless of truss, frame, or continuum models used for analysis. Furthermore, while the graphic statics method used for designing stiff trusses needs only the form diagram and a force diagram, our method requires two additional force diagrams. They correspond to the cases of unit virtual forces: one applied at the output point in the desired direction and the other in the orthogonal direction. The form diagram and three force diagrams enable the computation of individual contributions of truss members to the strain energy, output displacements in desired and orthogonal directions, and volume of the truss. Statically determinate and indeterminate truss topologies conceived intuitively or extracted from optimal continuum topologies are used for shape design. By interactively moving the vertices in one of the four diagrams and making corresponding the updates in the others, we change the shape of the truss to achieve multiple objectives. The efficacy of the method is demonstrated with examples and preliminary validation using 3D-printed prototypes.