Topology-optimization based design of multi-degree-of-freedom compliant mechanisms (mechanisms with multiple pseudo-mobility)

Unlike conventional mechanisms, compliant mechanisms produce the desired deformations by exploiting elastic strain and do not need, therefore, moving parts. The number of degrees of freedom of a conventional mechanism, also called mobility, is the number of independent coordinates needed to define a configuration of the mechanism. Due to the different operating principle, such definition of degree of freedom or mobility cannot be directly applied to compliant mechanisms. While those terms are not able to denote a property of a given compliant mechanism, they are meaningful when applied to the design of a compliant mechanism. Compliant mechanisms are, however, mostly seen as elastic structures, for which the term degree of freedom is used in a different meaning. In order to avoid ambiguities, the term pseudo-mobility (already introduced in previous published work) will be used to denote the number of scalar parameters needed to identify one single desired deformation, i.e. one single deformation for which the compliant mechanism is designed. Many synthesis approaches exist for compliant mechanisms with single pseudo-mobility (commonly referred to as "single degree of freedom mechanisms"). In the case of compliant mechanisms with multiple pseudo-mobility (multiple-degree of freedom mechanisms), only synthesis approaches for relatively simple mechanisms exist so far, while systems for more complex tasks like shape adaptation are not covered. In addition, only certain cases of transverse loads are included in the synthesis with these approaches. In this paper, a novel optimization algorithm is presented that addresses these two shortcomings. The algorithm is tested on a simple mechanism with one translation and one rotation kinematic degree of freedom, a compliant parallel mechanism for pure translation and a shape-adaptive structure.