Six-Bar Linkages with Compliant Mechanisms for Programmable Mechanical Structures

Programmable mechanical structures are formed by autonomous and adaptive cells and can reproduce meshes known from the finite element method. Furthermore, they can change their structure not only through morphing, but also by self-reconfiguration of the cells. A crucial component of the cells, which can preserve the underlying geometry of a triangular mesh, are six-bar linkages. The main part of the present contribution concerns the six-bar linkages as a fully 3D-printable compliant mechanism where each revolute joint of the six-bar linkage is replaced with a notch flexure hinge with the circular contour. The utilization of notch flexure hinges presents two significant drawbacks. First, notch flexure hinges do not maintain the center of rotation. Second, although compliance is an inherent and desirable characteristic of flexural hinges, it gives rise to secondary or parasitic motion. The compliance subsequently lead to alterations in the underlying geometry of a triangular mesh. For self-reconfiguration of the cells, an efficient model is needed to predict the positioning errors. Therefore, the flexure hinge is represented by three distinct models, namely a finite element model, a beam model, and a simplified linearized model based on translational and rotational spring elements. These models are compared and evaluated in succession first to identify the parameters of the simplified model and later on, the simplified model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The current work brings us closer to both the development of programmable mechanical structures and the prediction of positioning errors during self-reconfiguration.