Modeling Large Spatial Deflections In Distributed-compliance Compliant Mechanisms

Compliant mechanisms achieve specific motions through the elastic deformations of their flexible units.They are often used in mechanical systems that requires light weight,miniaturization,and high precision due to their advantages such as assembly-free,no friction and lubrication,etc...However,geometric nonlinearities due to large deflections of flexible units results in great challenges to model compliant mechanisms precisely.Therefore,accurate model for large spatial deflected flexible units are vital to guide the synthesize and analysis of compliant mechanisms.Beam flexures,which provide large deflections and small stresses,are commonly used as flexible units in compliant mechanisms which require large range motions.However,the lack of beam models that comprehensively include the geometric nonlinearities have severely restricted the development of compliant mechanism.In order to solve this problem,this dissertation focus on the accurate modeling of the large spatial deflection of the beam flexures.This dissertation puts forwards several works include:(1)Based on the Spatial Beam Constraint Model(SBCM)for bi-symmetrical cross-section beams,spatial beam constraint models for rectangular beams are proposed.By discussing the magnitude of the displacements and loads in the intermediate spatial deflections range for large aspect ratio beams,the simplified governing equations are derived.By solving the governing equations using the Power Series method and Taylor expanding the results with respect to the displacement components,closed-form load-displacement equations for large aspect ratio beams are obtained.A symmetric parallelogram flexible mechanism is modeled to demonstrate the validity of the model.Besides,a model which works for small aspect ratio beams is derived through Newton method.And the closed-form load-displacement equations are proposed.By comparing with the nonlinear finite element method,parameters in the load-displacement equations for small aspect ratio beams are proved to be correct.(2)By using the chained algorithm,the chained spatial beam constraint model is proposed to modeling large spatial deflections of beam flexures with rectangular cross-sections.By discretizing the beam flexure into several identical elements,each element can be modeled through the spatial beam constraint model.Geometric relations and load equilibrium equations between elements are build by using the space coordinate transformation.Combining the load-displacement equations for elements,the geometric equations and load-equilibrium equations between elements,the large spatial deflections of beam flexures can be modeled.This model realizes the decomposing the geometric nonlinear factors into different scales and reducing the difficulty of solving the governing equations for large deflected beams.Two examples are used to verify the correctness of the chained spatial beam constraint model by comparing with the nonlinear finite element method.(3)Chained spatial beam constraint models for large spatial deflected initially curved beams are proposed.Considering that the normalized curvature of beam elements decreasing by adding the quantity of element when discretizing the curved beam,the arc can be replaced by the corresponding chord,approximately.Therefore,the curved beam can be approximated modeled as a series of straight beam elements.By modeling the element with spatial beam constraint model and deduce the geometric relations and load equilibrium equations using the space coordinate transformations,the large deflections of curved beams can be modeled.Three examples that include curved beams are modeled using the method and the comparison with nonlinear finite element method has verified the correctness of the model.(4)Models that proposed in this dissertation are used to guiding the analysis and synthesis of compliant mechanisms.Analytical stiffnesses of parallelogram flexure mechanism in the directions of degree of freedom and degree of constraint are derived by using the spatial beam constraint model.Experiments have been designed to verify the correctness of the analytical results.A helix motion compliant mechanism with constant-force property is proposed.By modeling and optimizing parameters of helix motion mechanism using the chained spatial beam constraint model,a large constant-force range is obtained.By comparing with the results obtained by NFEA and experiments,the validity of these models are verified.