Spherical Five-bar Mechanism Based On Numerical Atlas Method Research On Scale Synthesis

The trajectory synthesis of spatial linkage is one of the important contents of linkage design.Compared with the planar linkage mechanism,the research on the spatial linkage mechanism is less,and the research on the spherical five-bar mechanism is even less.Therefore,this paper conducts in-depth research on the trajectory synthesis of the spherical five-bar mechanism.Firstly,the mathematical model of spherical five-bar type I mechanism is established,and the relationship between the input and output trajectory of the mechanism is derived.Based on the Fourier series theory and one-dimensional Fourier series properties,the harmonic transformation of the trajectory is carried out to obtain the characteristic parameters of the trajectory curve.According to the properties of the spherical curve itself,it is standardized to eliminate the influence of factors such as the length,shape and installation position of the spherical five-bar mechanism,so as to find the relationship between the connecting rod trajectory and the basic size of the mechanism.On this basis,the adaptive atlas library of input and output trajectory characteristics is established by numerical atlas method.By comparing the similarity between the given curve and the characteristic parameters in the atlas library,the target mechanism with the highest similarity is identified.With the help of the derived theoretical formula,the parameters such as the actual rod length size and the actual installation position of the mechanism are inversely calculated to realize the trajectory synthesis of the spherical five-bar mechanism.The correctness of the proposed method is proved by theoretical examples.By comparing the examples,the motion simulation test is carried out with the Motion simulation in Soildworks,which proves that the output of the spherical five-bar mechanism is rich.Secondly,the mathematical models of spherical five-bar type I type II mechanism and spherical five-bar type II mechanism are established respectively.According to the above methods,they are standardized,feature parameters are extracted,adaptive library is established,the optimal solution is identified and optimized,and the parameters of the actual installation position are solved.Then,the correctness of the proposed method is proved by theoretical and comparative examples.Based on this method,the trajectory synthesis problem of these two types of spherical five-bar mechanisms is solved.Finally,according to the comprehensive examples of three types of spherical five-bar mechanisms,the correctness and effectiveness of this method on the trajectory synthesis of spherical five-bar mechanisms are proved.