Automated Generation Of Kinetostatic Models For Planar Flexure-based Compliant Mechanisms

Flexure-based compliant mechanisms(FCMs)are a special class of mechanisms that utilize flexure hinges as their flexible members to transfer or convert motion,force and energy.The advantages of such mechanisms over traditional rigid-body mechanisms include miniaturization of components,elimination of friction,wear,backlash and noise,reduction of or no need for lubrication,assembly and maintenance,and the improvement of precision and reliability.They have been widely employed in advanced manufacturing,optical engineering,biomedical,aerospace and other fields,which have become one of the core technologies of high-end equipment and play an important role in the field of precision engineering.Design,analysis and modeling of FCMs are more challenging than that of traditional rigidbody mechanisms because their motion is always accompanied by the complex deformation of the flexure hinge.In this paper,an in-depth and systematic research on FCMs from automatically generating kinetostatic model(based on two-colored digraph and matrix method),optimization of structural size,experimental testing to software analysis are carried out.The FCMs can be divided into the rigid link and flexure hinge which are the smallest elements,then the geometric equations of a serial flexure-based compliant mechanism composed of multiple rigid links and flexure hinges are derived based on the deflection formulation of a flexure-link module.The rigid link and flexure hinge can be also formed binary link,ternary link or multinary link,and the equations of static equilibrium are constructed respectively for each link.All the derived formulas show a unified form,and the laws contained in them lay a theoretical foundation for the automatic generation of the kinetostatic model and the development of the software platform in the following chapters.An improved two-colored digraph for planar flexure-based compliant mechanisms is presented,to more clearly and accurately reflect the topological relationship of the mechanism.By utilizing the data structure of orthogonal list stored on the computer,and traversing the vertices and edges of the digraph in the required order,the kinetostatic models for planar flexure-based compliant mechanisms can be automatically generated.According to the definition of link-flexure incidence and path matrix,the corresponding matrix is written.The geometric equation of the mechanism is derived from the path matrix.The concept of “virtual flexure hinge”is first proposed,and the unified static equilibrium equation is obtained by the incidence matrix with the virtual flexure hinge.The complex problem of kinetostatic analysis of FCMs is transformed into a vivid,simple and unified matrix representation.The processes of automatically generating kinetostatic model for planar FCMs based on two-colored digraph and matrix method are illustrated by a number of representative mechanisms,and the results are compared with the results of the energy method and the finite element method to demonstrate the accuracy and effectiveness of the proposed method.Based on the proposed approach,a software for automatically generating kinetostatic models of planar FCMs is developed to provide a reference for users to forecast,evaluate and improve their mechanisms.The software mainly includes information input module,calculation module and post-processing module,and its effectiveness is verified by simulation and experiment.An optimization model is developed aiming at improving the static performance of the FCM.Its objective is to determine the distribution positions and geometrical characteristic parameters of flexure hinges that takes the kinetostatic model as the constraint condition.A novel two-stage differential micro-displacement amplification mechanism is designed by using the optimization model.The prototype,according to the optimized results,is manufactured.The experiment platform is set up,and the amplification ratio of the prototype is tested.Results of the experiment and the finite element simulation verify the correctness of the theoretical model.