Dimensional Synthesis Of Planar Linkage Mechanisms Based On Wavelet Series

Linkage mechanism is essential in mechanical transmission.It plays an important role in many applications such as engineering fields,electromechanical integration,agricultural modernization and military defense system.Numerous methods for the dimensional synthesis of linkage mechanism have been proposed.However,in many conditions,more attention is given to non-integer-period dimensional synthesis than integral periodic dimensional synthesis.So non-integer-period dimensional synthesis is more noteworthy.The aim of this work was to propose a new numerical atlas method to apply to the non-integer periodic motion generation of a four-bar mechanism and multiple tasks synthesis of planar multi-loop linkage mechanisms.Contrasting with earlier work,this new method has advantages in the accuracy of analytic geometry and the simplified computation method of the numerical atlas.The limitation of the Fourier series in not describing the non-integer periodic motion generation well can be overcome.Non-integer-period motion generation of a planar four-bar mechanism.Firstly,on the basis of the theory of the Haar wavelet series,the early proposed method,which is used to solve the problem of planar four-bar path synthesis,is extended to motion generation synthesis of a planar four-bar mechanism.By analysing the wavelet coefficients between the rigid-body rotation angle and the connecting rod rotation angle of its corresponding basic dimensional types,the internal relationships are determined.Based on this finding,an output feature parameters database of planar four-bar motion generation including 101408 sets of the basic dimensional types was established.Using the fuzzy identification method and theoretical formulas to compute the actual size and installing positions parameters of a planar four-bar mechanism,the synthesis of a planar four-bar motion generation mechanism can be achieved using the established numerical atlas,fuzzy identification method and theoretical formulas.Dimensional synthesis of multiple tasks of a planar six-bar linkage mechanism.Secondly,a method for multiple tasks synthesis of a planar six-bar linkage mechanism by wavelet series is presented.Based on the theory of wavelet series,a mathematical model for the multiple tasks output of planar linkage mechanisms was established.The multiple tasks which combine a function generation and a rigid body guidance will be presented throughout this paper.For function generation,based on the relationships of the wavelet feature parameters,a numerical atlas database including 31775 groups of basic dimensional types of a planar slider-crank mechanism was established.For rigid body guidance synthesis,by analysing the relationships of the wavelet coefficients between rigid body rotation angle and connecting rod rotation angle of its corresponding basic dimensional types,an output feature parameters database of a planar four-bar motion generation including 178810 groups of the basic dimensional types was established.Using the fuzzy identification method and theoretical formulas to calculate the actual sizes and installing positions parameters of planar multi-loop mechanisms.Finally,two examples are presented to illustrate the validity and practicality of the proposed theory.