Dimensional Synthesis Of Linkage Mechanism Using Output Wavelet Feature Parameters

Dimensional synthesis is a classical research field of linkage design.Comparing with the analytical methods,the numerical atlas methods can be applied to solve the problems of infinitely separated positions in theory.Moreover,the methods avoid the problems of solving nonlinear equations,selecting optimal initial values and convergence of iteration.The main advantages of the numerical atlas methods are intuitive and simple.However,there are few studies on the application of numerical atlas methods to solving the problems of nonperiodic dimensional synthesis of linkage mechanisms.Based on the wavelet theory,a dimensional synthesis method is proposed in this paper for solving nonperiodic design requirements problems.First of all,the use of Daubechies wavelets to describe open curves,including nonperiodic output functions curves and coupler curves,is presented.The geometric significance of a wavelet approximation and a wavelet detail for nonperiodic output function curves and coupler curves of linkage mechanisms are given.By analyzing the internal relationship of the output curves with corresponding wavelet coefficients,a description method is established for output function curves and coupler curves of linkage mechanisms using output wavelet feature parameters.Secondly,the mathematical models of linkage mechanisms,including planar four-bar mechanism,spherical four-bar mechanism,spatial RSSR mechanism and RCCC mechanism are established.By analyzing the wavelet coefficients of output function curve of four-bar mechanism,the relationship between the basic dimensional types and the wavelet details are found.Based on this finding,the self-adapting numerical atlas databases of planar four-bar mechanism,spherical four-bar mechanism,spatial RSSR mechanism and RCCC mechanism are established.Based on the relationship of wavelet coefficients between the prescribed function curve and output function curve generated by basic dimensional types,the actual sizes and installation positions of desired linkage mechanism can be obtained.Moreover,the nonperiodic function generation of planar four-bar mechanism,spherical four-bar mechanism,spatial RSSR mechanism and RCCC mechanism are also performed.Thirdly,a mathematical model of coupler curve of planar four-bar mechanism is established.A feature parameters extraction method for coupler curves is proposed using preprocessing,the wavelet transform and normalized method.Then,the effects of mechanism transformation on the feature parameters can be eliminated,including a change of size,absolute position and orientation.A self-adapting numerical atlas database for coupler curve of planar four-bar mechanism is established.Then,the open path synthesis method is extended to spherical four-bar mechanism and spatial RRSS mechanism.A high-dimensional path generation problem is translated into a lower-dimensional matching recognition problem and an actual size and installation position calculation problem.The self-adapting numerical atlas databases for coupler curve of spherical four-bar mechanism and spatial RRSS mechanism are established.Based on the position relationship between the prescribed open path and the coupler curve generated by the feature dimensional types,the actual sizes and installation positions of desired linkage mechanism are calculated.The open path generation of planar four-bar mechanism,spherical four-bar mechanism and spatial RRSS mechanism are realized.Finally,based on the method proposed in this paper,combing with a Fourier series method,a computer aided design system for dimensional synthesis of linkage mechanism,including planar linkage mechanism,spherical linkage mechanism and spatial linkage mechanism,is developed using Matlab graphical user interface(GUI).Particularly,a roller feed mechanism for roller hemming is designed and manufactured to verify the validity and practicality of this method.The design results provide new ideas for the roller hemming.