Integrated Design Method For Topological And Dimensional Synthesis On The Basis Of Motion Geometric Constraints For 1-DOF Planar Mechanism

Mechanism kinematics synthesis is an important research direction in mechanism kinematics research.The synthesis of mechanism is mainly divided into two parts: topological synthesis and dimensional synthesis.The selection of the configuration of mechanism and the type of kinematic pairs constituting mechanism is called topological synthesis,and the solution of structural parameters and unknown parameters of components is called dimensional synthesis.The two parts are related to each other and constitute the main content of mechanism motion synthesis.However,both configuration synthesis and dimensional synthesis have their own limitations.Therefore,in order to obtain the best mechanism type and size of mechanism at the same time,how to synthesize both topology and dimension is a major difficulty in mechanism motion synthesis research.In this paper,kinematic synthesis of planar mechanisms is studied based on the method of motion geometric constraints,and the general quadratic constraints(straight line,circle,ellipse,hyperbola,parabola)of planar motion are analyzed.A unified mathematical model based on motion geometric constraints is established,and the theoretical derivation of plane kinematic synthesis method based on motion geometric constraints is completed.At the same time,based on the theoretical method,homotopy algorithm is used to solve the problem,and the constraints equation is matched with the corresponding mechanism.At the same time,configuration synthesis and dimensional synthesis are completed,which verifies the correctness of the theoretical method.The main work and achievements of this paper are as follows:Geometric elements in common mechanisms and bar groups are extracted,and the kinematic geometric constraints of planar mechanisms and their algebraic expressions at the mathematical level are obtained,and the image properties of quadratic curves are analyzed.The general quadratic constraints(straight line,circle,ellipse,parabola,hyperbola)are studied and analyzed,and the corresponding constraints of general quadratic curves of planar mechanisms are obtained.The motion synthesis theory of planar mechanism based on motion geometry constraints is briefly described.A unified mathematical model of planar mechanism motion synthesis including practical engineering constraints is constructed.The basic principle of homotopy algorithm is introduced and solved by homotopy algorithm.The matching between constraint equation and corresponding mechanism is completed according to the solution result,and the unification of topology synthesis and dimensional synthesis is realized.A simple human-computer interaction interface is designed by MATLAB,and examples of five,six and seven target pose motion synthesis are demonstrated by using the interface.The user can clearly understand the flow of the motion synthesis method introduced in this paper,and the feasibility of the motion synthesis method introduced in this paper is verified.