A family of multi-stable mechanisms based on the threefold-symmetric Bricard linkage

Multi-stable structures capable of switching among stable states play an important role in various engineering applications. By extending the discrete stable state into a finite range of mechanism motion so as to create a multi-stable mechanism, the deformation capability can be substantially enhanced to enable functions such as large deployable ratios, but the relevant design theory has not been fully established. Here, by utilizing the intrinsic physical blockage during the motion of the threefold-symmetric Bricard linkage, we propose a family of multi-stable mechanisms that have both finite mechanism motion ranges and discrete stable states. A kinematic analysis is first conducted to characterize the physical blockages in their motion paths. Then, by replacing a set of conventional revolute joints with stretchable elastic membranes to overcome physical blockages, two types of multi-stable mechanisms are designed. The first allows two stable states respectively at the fully deployed and folded configurations and a continuous mechanism motion range in between, while the second exhibits two mechanism motion ranges separated by an energy barrier. A theoretical model is built to program the mechanism motion range and energy threshold of the multi-stable mechanisms, which are verified by experiments and numerical simulations. This work is expected to open up a new avenue for the development of multi-stable mechanisms, broadening their application across diverse engineering fields.