Study On Dimensional Synthesis Of Spatial Mechanism By Harmonic Characteristic Parameters

The dimensional synthesis of linkage mechanisms is the main content of linkage mechanism design. The research about the dimensional synthesis of the planar linkages is quite systemic and in-depth; however, the research on spatial linkages is relatively less. So the method of dimensional synthesis of the spatial linkages is studied systematically and deeply in this dissertation.Firstly, based on the geometric properties of one-dimensional and two-dimensional Fourier series, a geometric constraint conditions are proposed to establish the three-dimensional Fourier series. The geometric meanings of mechanism for Fourier series are put forward. The expression of coupler curve can be obtained by the expression of three-dimensional Fourier series and Fourier transform. The problem about mathematic representation of the coupler curves of spatial mechanism is resolved.Secondly, the geometrical model of spherical four-bar linkages is proposed, the harmonic component of the coupler curves is analysed by using the Fourier series theory. The relationship between the harmonic component of the coupler curves and the harmonic component of the rotation-angle function and the dimensional type of spherical four-bar mechanism is discovered. A process of normalization was applied in order to eliminate the effects of scale, translation, rotation and input-crank start angle in both the basic dimensional type and the dimensions of the original mechanism. Based on the basic dimensional type of spherical four-bar linkages, a numerical atlas database of harmonic characteristic parameters of the spatial four-bar linkages is build up. The formulas which can compute the position for coupler point, real size and installing dimensions of the spherical four-bar mechanism is deduced. Based on those theoretical formulas and the numerical atlas database of the harmonic characteristic parameters, the problem of path synthesis of spherical four-bar mechanism is solved.Thirdly, the input-output function of spherical four-bar linkages is investigated systematically by using the Fourier series method in this dissertation.The relationship between the harmonic component of the input-output function and the dimensions of the spherical four-bar linkages is established. Based on this relationship, the basic dimensional type of spherical four-bar linkages is determined. The problem of function synthesis of the spherical four-bar linkages is solved by setting up the numerical atlas database, which comprises 490545 basic dimensional types, and given the concrete steps of the function generator. Using the similar method, the dimensional synthesis of single degree of freedom spatial mechanisms (the RCCC mechanism, RRSS mechanism and RSSR mechanism) is discussed. Through the above study, the numerical atlas method for dimension synthesis of spatial mechanism is formed.Finally, a unified approach of dimension synthesis is established by means of the Fourier series method, and the unified mathematical model of the mechanism synthesis is set up, which includes planar, spherical and spatial linkage. The concepts of the coupler rotation-angle operator, mechanism's basic dimensional types and harmonic characteristic parameters of dimensional type offer a theoretical basis to establish the numerical atlas database of linkage mechanism. The derivation process of formula, which can compute the position for coupler point, real size and installing dimensions of the linkage mechanism, is presented.