Deformation Calculation Of Spatial Large Deflection Beam And Its Application On The Modeling Of Spatial Compliant Mechanisms

Spatial compliant mechanisms have large working space, wide range of motion and can accomplish complex tasks beyond what planar linkages are capable of performing. There have been many applications in the fields of precision instruments, medical and biological mechanisms. However, the nonlinearity associated with the spatial large-deflection beams(especially the coupling between bending and torsion) during the motion of a spatial compliant mechanism often complicates its modeling and design.According to the bending and torsion analysis of planar curved beam with circular section,this dissertation discusses the deformation of infinitesimal ds of the curved beam, and two kinds of load are provided which forced the infinitesimal ds deformed as a spatial curve.Based on the theoretical basis of space curve, Bernoulli-Euler beam theory and Hooke’s law, the nonlinear governing differential equations(GDEs) and boundary constraint conditions and orientation of the beam cross-section for the spatial large-deflection beam are formulated.The governing differential equations and boundary conditions for spatial large-deflection beam can be treated as an initial value problem of ordinary differential equations. As there are some unknown parameters in the GDEs, two numerical integral methods(RKF45-PSO and RKUO) are proposed to solve the GDEs based on the optimization algorithm. The detailed solving steps and flow charts are also provided. The RKF45-PSO and RKUO results are validated by a spatial pseudo-rigid-body model(PRBM) method and nonlinear finite element analysis(NFEA)(including ANSYS and ABAQUS).For the nonlinear large deflection problem of spatial rectangular cross-section beam, this dissertation discusses the influences of oblique bending on the large deflection of spatial beam, and analyzes the coupling between the nonlinear bending and torsion. Then the GDEs and corresponding boundary conditions for spatial large deflection beam are formulated. The orientation of the beam cross section is also analyzed with three Euler angles.As the complex of the GDEs and there are many variables during the reverse solving, a numerical method(RKF45-LMA) is proposed based on the Levenberg-Marquardt algorithm. The flow charts are also provided and the solving processes are discussed in two cases. The accuracy and effectiveness of the RKF45-LMA results are validated by the NFEA.Then, the kinetostatics models of a partial compliant four-bar mechanism, a tension spring and a spatial circular guided compliant mechanism are developed using the GDEs of spatial large-deflection beam, and solved by the RKF45-PSO or RKF45-LMA. The accuracy and effectiveness of the solving method are validated by the NFEA, 3R PRBM method and experimental results.Finally, based on the analysis of the free end path of the spatial large deflected beam, a spatial pseudo-rigid-body model(SPRBM) is proposed to model the large deflection of the spatial beam. Three pseudo-rigid-body springs with bending and torsion deformation are used to predict the spatial beam-end path and the orientation of the beam cross section. The characteristic parameters of the spatial pseudo-rigid-body model are obtained through an optimization process. The effectiveness and capabilities of the SPRBM are validated by modeling of spatial compliant mechanisms and comparing with the RKF45-LMA results.In conclusion, the GDEs and the corresponding numerical solving methods for the spatial large-deflection beam are high efficiency, accuracy and have better convergence, which provide a feasible method for accurately modeling of spatial compliant mechanisms.