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

Abstract

Unlike conventional mechanisms, compliant mechanisms produce the desired deformations by exploiting elastic strain. The mobility of a conventional mechanism is the number of independent coordinates needed to define a configuration of the mechanism. The corresponding concept applicable to compliant mechanisms is the so-called pseudo-mobility defined as the number of scalar parameters needed to identify one single desired deformation of a compliant mechanism. In the case of compliant mechanisms with multiple pseudo-mobility, 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 a limited choice of transverse loads are considered in those approaches. In this paper, a novel optimization algorithm is presented that addresses these two shortcomings. This algorithm is based on a two-step iterative procedure in which the load-case dependency of the deformation is minimized and desired deformations are imposed. The algorithm is tested on mechanisms of different complexity. It could be demonstrated that the new procedure is well suited for the synthesis of different types of compliant mechanisms.

Topology Optimization-Based Design of a Sensor-Integrating Feather Key

“…The structure with the highest selectivity (S = 1.93) and its existing first two eigenmodes are shown in Figure 3. The first two eigenmodes of this structure (Figure 3 (b) and (c)) are similar to the desired first eigenmodes, but there is more deviation than in previous optimizations of other CMs with multiple pseudo-mobility [6] due to the high primary stiffness required. However, the deviation of the eigenmodes is negligible if the kinematic instead of the desired eigenmodes are included in the further considerations.…”

“…As explained earlier, the feather key is to be optimized as CM with selective compliance and multiple pseudo-mobility. As such, it must have characteristic properties [6], which are briefly described below. The DoFs of the structure to be optimized are discretized to p DoFs.…”

“…To achieve the goals mentioned in the previous section, the optimization procedure presented in [6] is used. For this, first a design space is defined, which is filled with r finite elements.…”

“…Therefore, it is divided into two subproblems that are iterated stepwise one after the other to enable an efficient solution of the problem. A run of both subproblems is called an iteration step s. The detailed description of the two subproblems can be found in [6]. The optimization proceeds as follows: first, a starting vector for the design variable x 0 is given.…”

“…This quantity cannot be readily applied to CM. However, there is a quantity that is similar to it: the pseudo-mobility m. This specifies for how many independent desired deformation patterns a CM is designed [6]. During optimization, the desired motion and defined load cases are imposed on so-called input and output degrees of freedom (input and output DoFs).…”