Nonlinear Design of a General Single-Translation Constraint and the Resulting General Spherical Joint

Abstract Compliant mechanisms, such as compliant spherical parallel joints, play a vital role in engineering applications, often relying on single-translation constraint wire beams. However, these wire beams have inherent shortcomings, such as manufacturing challenges and low axial stiffness. Addressing these issues is imperative and first leads to the nonlinear design of the General Single-Translation Constraint (GSTC) leaf beam in this paper, which offers versatility in creating diverse single-translation constraint leaf beam configurations through geometry parameter manipulation. Leveraging the GSTC leaf beam, we then designed a versatile compliant-mechanism-based general spherical joint (spherical parallel mechanism) by introducing four key parameters. The spatial kinetostatic models of the GSTC leaf beam and the general spherical joint were both formulated using a nonlinear spatial beam constraint model. Four representative specific configurations derived from the general spherical joint were further selected for finite element analysis (FEA) verification and performance comparative analysis with a focus on the center drift. Finally, an experimental hardware was set up to test a fabricated prototype of the L-shaped beam-based spherical joint for the load-dependent effects and the nonlinear center drifts. The experimental results confirm the high accuracy of the proposed nonlinear spatial models, which can facilitate model-based, rapid multi-objective optimization in future studies.