Modeling large spatial deflections of slender bisymmetric beams in compliant mechanisms using chained Spatial-Beam-Constraint-Model (CSBCM)

Modeling large spatial deflections of flexible beams has been one of the most challenging problems in the research community of compliant mechanisms. This work presents a method called chained spatial-beam-constraint-model (CSBCM) for modeling large spatial deflections of flexible bisymmetric beams in com- pliant mechanisms. CSBCM is based on the spatial beam con- straint model (SBCM), which was developed for the purpose of accurately predicting the nonlinear constraint characteristics of bisymmetric spatial beams in their intermediate deflection range. CSBCM deals with large spatial deflections by dividing a spatial beam into several elements, modeling each element with SBCM, and then assembling the deflected elements using the transforma- tion defined by Tait-Bryan angles to form the whole deflection. It is demonstrated that CSBCM is capable of solving various large spatial deflection problems whether the tip loads are known or the tip deflections are known. The examples show that CSBCM can accurately predict the large spatial deflections of flexible beams, as compared to the available nonlinear FEA results ob- tained by ANSYS. The results also demonstrated the unique ca- pabilities of CSBCM to solve large spatial deflection problems that are outside the range of ANSYS.