Efficient spatial compliance analysis of general initially curved beams for mechanism synthesis and optimization

Compliant Mechanisms (CMs) present several desired properties for mechanical designs. Conventional rigid-body mechanisms composed of rigid links connected at kinematic joints, serve as devices to transfer motion, force and energy by the movements of rigid links whereas CMs are able to present the same function only through deflection of flexible members. Most designs of CMs in the current literature employ straight beams as the elementary flexible members whereas initially curved beams (ICBs) also provide potential advantages for CMs such as large range of motion and small strain range. This paper presents an efficient spatial compliance analysis method of general ICBs. The spatial compliance analysis of different types of ICBs (such as varying-curvature beams and varying-cross-section beams) was conducted, followed by Finite Element Analysis (FEA) verification. Next, the modeling and optimization of two types of CMs including ICB-based parallelogram mechanisms and ICB-based Ortho-planar springs were carried out by applying screw theory under the framework of position space concept and parameter normalization strategy where a class of anti-buckling translational parallelograms with high load-bearing capacity and a type of compact 2R1T (2 rotational DOF and 1 translational DOF) compliant kinematic joints were obtained. The corresponding FEA was conducted to verify the optimal results.