Path Synthesis Method Of Four-bar Linkage Based On Trajectory Feature Ellipse

The synthesis method of linkage mechanism is an important basic research of mechanism theory.Four-bar linkage is one of the simplest and most commonly used linkage mechanisms.It pays more attention to the track synthesis of its output in the popular industrial production application.Therefore,based on the elliptic and numerical atlas method of the trajectory characteristics of the four-bar linkage,this paper studies the trajectory synthesis of the planar and spatial linkage mechanism(planar four-bar linkage mechanism and spatial RRSS mechanism)respectively.Firstly,the mathematical model of planar four-bar linkage trajectory is established.Through the analysis of the coupler curve,it is found that each point on the trajectory curve of the planar four-bar linkage at the standard installation position corresponds to the corresponding rotation input angle,and the trajectory point after rotation is located on the circular curve,which is defined as the trajectory feature circle.Based on this finding,the path synthesis problem of planar four-bar linkage at general installation position can determine the length of the input member,the length of the links and the installation position of the desired mechanism by optimizing the feature circle approximation function.Then the target trajectory is translated to determine the installation location parameters.With Fourier transform as the tool of translation free installation position parameters of link path of planar four bar linkage harmonic analysis mathematical model,to establish the basic dimensional types include planar four-bar linkage and the size of the corresponding harmonic characteristic parameters of the numerical atlas,by using the method of fuzzy recognition of planar four-bar linkage that could get the required basic length size.Then,according to the relationship between the optimization results of the characteristic circle approximation function and the basic dimensional types,the remaining dimensional types are calculated to realize the comprehensive study of the coupler link trajectory of the planar four-bar mechanism.A numerical example is given to confirm the effectiveness of the proposed method.Secondly,the mathematical model of coupler curve of the spatial RRSS mechanism at the standard installation position was analyzed.The projection points of the trajectory curve on the plane xoy rotated the corresponding input Angle around the z-axis,and the generated points lie on an elliptic curve,which was defined as the trajectory feature ellipse.Based on the findings,the establishment of institutional database installation position rotation Angle,the target trajectory sampling and rotation angle is set in the database,in order to rotate after the preprocessing of sample point calculating trajectory characteristics of elliptic curve,comparison of characteristics of elliptic curve and the same position error and the minimum path curves after pretreatment,then the desired installation angle is determined.This paper analyzes the mathematical model of linkage trajectory without installation Angle parameters,establishes the dynamic numerical atlas database of linkage trajectory with Fourier transform as the tool,determines the basic dimensional types of spatial RRSS mechanism of target trajectory through fuzzy recognition method,and then calculates the actual size and installation position of the target mechanism according to the theoretical formulas.An example is given to illustrate the correctness of the method.Finally,the phase Angle of the trajectory feature ellipse of the planar four-bar mechanism and the spatial RRSS mechanism above is processed and defined as the feature parameters of the desired mechanism.Then,through harmonic analysis,the numerical atlas library of the angle of the four-bar mechanism coupler is established,and the path synthesis of the four-bar mechanism is accomplished by using the numerical atlas method.A number of examples are given to demonstrate the feasibility of the proposed method for trajectory synthesis of four-bar linkage.