Optimized design of generalized flexure rotational couplers

Four-bar linkages can transmit angular motion between two rigid links, but their transmission ratio is generally not constant due to kinematic nonlinearities. When such linkages are implemented with flexures – replacing joints with elastic elements to eliminate friction, backlash, and wear – additional parasitic motions are introduced. This article demonstrates that nonlinearities arising from both rigid-body kinematics and flexure deformations can be harnessed to compensate for one another, leading to optimized flexure-based couplers, inversors, reducers, and amplifiers. The analytical model merges Euler–Bernoulli beam theory with loop-closure kinematics, providing geometric design rules that exploit these nonlinear effects to improve transmission constancy. Finite element modeling and experiments on polymer prototypes confirm the validity of the approach, showing that optimized flexure couplers can match or even surpass the performance of ideal four-bar linkages. For instance, in a flexure mechanism with a 1:−1 transmission ratio, the error is reduced from 23% to below 1% for angular displacements up to ±20°. These results establish flexure-based transmission mechanisms as a new class of kinematic building blocks for the design of purely rectilinear and purely circular flexures.