The Spatial Linkage Based On Fourier Series Synthesis Of Rigid Body Guidance

Spatial linkage mechanism is widely used in industrial production because of its simple structure and low cost.The traditional spatial linkage mechanism scale synthesis research method has been very popular,but in many practical applications,we pay more attention to the rigid-body guidance problem in the output.Compared with the traditional research method of rigid body guidance synthesis,the numerical map method is more intelligent and automatic.However,there is not a detailed flow chart and a unified definition for the research on the rigid body guidance synthesis of spatial linkage mechanism by using the numerical map method.Therefore,this paper combines the Fourier series theory to divide different spatial linkage mechanisms into RCCC mechanisms and RRSS mechanisms.Do not conduct comprehensive research on rigid body guidance.A unified research method based on Fourier series theory and numerical atlas is applied to the rigid body guidance synthesis of spatial linkage mechanism.First of all,according to the rigid body guidance requirements of spatial RCCC linkage mechanism,the geometric model of rigid body guidance is drawn,and its mathematical model is arranged according to the variable relation in the geometric model,and the angle function of connecting rod is extracted by Fourier series theory.The basic dimension type and its corresponding harmonic characteristic parameters are found by using the relationship between the harmonic characteristic parameters of the standard installation position and the general position angle output function,and the basic dimension database of the rotation angle is constructed.According to the given characteristic parameters of rigid body rotation angle,the required basic dimension type of rotation angle is selected,and then the position problem is transformed into a trajectory problem,and the final basic dimension is screened out by using the rigid body guiding position requirement.Based on the calculation formula of actual size,this paper calculates the actual size and realizes the comprehensive research on rigid body guidance of RCCC mechanism.The feasibility of this method is proved by an application example.Secondly,the geometric model and mathematical model of spatial RRSS mechanism are established.Through the model,the quantitative relationship between harmonic characteristic parameters of standard installation position and general position is found,and the basic dimension type of rotation angle and corresponding harmonic characteristicparameters are determined.The database of rotation angle numerical atlas is established,and the basic dimension type of rotation angle is selected in the numerical atlas library by the given rigid body rotation angle characteristic parameter,and then the position problem is transformed into the trajectory problem.According to the position requirement of rigid body,the basic dimension type satisfying the design condition is identified,and the calculation formula of actual dimension is deduced and the actual dimension is calculated.Thus,the rigid body of the given spatial RRSS mechanism is synthesized by the guidance of the rigid body of the given spatial RRSS mechanism.A practical example is used to ensure the correctness of the method.Finally,by analyzing and unifying the above research on the rigid body of the spatial RCCC-RRSS linkage mechanism,a unified mathematical equation of the rigid body rotation angle output and the rigid body position output of the spatial linkage mechanism is established.Based on the Fourier series theory,the quantitative relations of harmonic characteristic parameters corresponding to the basic dimension type and rigid body guiding mechanism are summarized,and the general steps for establishing the numerical atlas database by this relationship are given.Based on the quantitative relationship between harmonic characteristic parameters,the calculation methods of the real position of the integrated reference point of rigid body guidance of spatial linkage mechanism,the parameters of the actual mechanism and the actual installation size are summarized.The concept involved in this method is defined in a unified way,and a complete and unified numerical map method for the study of rigid body guidance of spatial linkage mechanism is concluded.