Multi-pose Motion Synthesis Method And Experiment Of Mechanism Based On Multivariate Function Extreme Value Theory

Mechanism as the core and foundation of mechanical equipment,its function and performance directly determine the competitiveness of mechanical products.As the functional requirements of mechanical equipments in various fields become more and more diverse,the motion law that the mechanism can realize is also more complex.In the field of agricultural machinery,the core mechanism of automatic transplanting equipment is planar linkage and unequal speed planetary gear train.What it requires is that the output component can realize a specific motion trajectory and posture,so as to replace a serie of actions such as picking,sending,and planting seedlings by hand.Designing a mechanism by a specific motion trajectory and posture is a typical mechanism motion synthesis problem.However,the current motion synthesis theoretical methods still have some deficiencies in some aspects,such as the applicable objects(linkage or gear train mechanism),range(exact,approximate,mixed synthesis),and the diversity of solutions(unique,finite,infinite solution),and lacks certain completeness and universality.For the requirements of multi configuration,position and working conditions in practical engineering,the synthesis method is often not applicable,and there are few or even no feasible solutions for the mechanism scheme.Therefore,based on related research at home and abroad,this dissertation takes the planar linkage and unequal speed planetary gear train mechanisms widely used in modern mechanical equipments as the research object.Firstly,a multi-pose motion synthesis method of planar serial chain based on multivariate function extreme value theory and homotopy algorithm is proposed to realize the multi solution of mechanism parameters;Secondly,based on the synthesis of serial chain,the motion synthesis of planar linkage and unequal speed planetary gear train with multi-pose constraint are realized,and the corresponding defect discrimination method is given;Finally,the proposed method is applied to the innovative design of the automatic transplanting mechanism for dryland plug seedlings in the field of agricultural machinery.The main research contents of this dissertation are as follows:(1)A multi-pose motion synthesis method of planar serial chain based on multivariate function extreme value theory and homotopy algorithm is proposed.Firstly,the extreme value theory method of binary function is extended to multivariate(> 2)function,the necessary and sufficient conditions for the existence of extreme value of multivariate function are discussed.The specific solution method and calculation example for obtaining the minimum value of multivariate function are given.Secondly,according to the displacement matrix and the constraint conditions of link pair,the N-pose motion synthesis equations of 2R and 3R serial chains are derived,and the relationship between the number of synthesis equations and parameters to be solved under different number of poses is analyzed.The approximate multi-pose motion synthesis of 2R serial chain is transformed into the extreme value problem of multivariate function,and the solution space is expanded by introducing variables to make it have multi solution.The approximation,hybrid multi-pose synthesis and error evaluation methods of planar 2R serial chain are given.Finally,it is pointed out that the precise multi-pose synthesis of 3R serial chain can specify up to six design parameters arbitrarily,and the transformation of its motion synthesis under different design parameters is discussed in detail.(2)The motion synthesis,analysis and defect discrimination methods of six bar inner planar linkage mechanism are given systematically.Firstly,the configuration characteristics of different linkages including planar four,five and six-bar linkages are analyzed.The motion synthesis idea of considering the planar closed chain linkage as the combination of several serial chains is proposed.The multi-pose motion synthesis of 2R and 3R serial chains are carried out respectively,and then the synthesis of closed chain linkage is completed,and the specific synthesis steps are given.Secondly,based on establishing the kinematic analysis model,the identification process of the dead point,circuit and branch of each linkage is analyzed by using the elimination and discriminant methods,and the input / output(I/O)curve of each link of the linkage are drawn.By judging whether the rotation angle value of the coupling link is located on the same branch of the same circuit,the defects of the synthesized mechanism are identified and eliminated.Finally,the specific synthesis examples of planar four-bar,geared five-bar,and six-bar linkages are given to verify the feasibility of the proposed method.(3)Extending the multivariate function extremal synthesis method of planar serial chain to the multi-pose motion synthesis of unequal speed planetary gear trainFirstly,the typical configuration and working principle of single and double planet carrier unequal speed planetary gear train are introduced.The single and double planet carrier unequal speed planetary gear trains are simplified into 2R and 3R serial chains respectively.All real solutions are obtained based on the multi-pose synthesis method of serial chain.Secondly,the relative angular displacement data of each link are calculated from the parameters of the serial chain obtained by motion synthesis.Based on this,the full turnover defect discrimination matrix of the gear train is established.The defect discrimination and configuration matching of the gear train mechanism are realized by judging the monotonicity of the data in each row of the matrix.Finally,the specific design process and examples of non-circular gear are given,including the calculation and distribution of transmission ratio,and the solution and optimization of pitch curve.The multi-pose motion synthesis of unequal speed planetary gear train is completed.(4)Innovative design and experiment of automatic transplanting mechanism for plug tray seedlings in dry landThe automatic picking and planting mechanisms in the dryland plug seedling transplanter in the field of agricultural machinery are taken as the objects.According to their operation requirements,a variety of ideal trajectories for transplanting operations are planned and designed,and special poses such as clamping,pulling,bringing,throwing,planting seedlings and returning are determined.Based on the above motion synthesis theory and method,a set of linkage and gear train seedling picking and planting mechanisms are synthesized respectively,and their structure design and modeling simulation are carried out.Through comparative analysis,the simulation results are basically consistent with their theoretical designs,which verifies the correctness of the synthesis method.Finally,the machining of the physical prototypes of the gear train seedling picking and planting mechanisms are completed,and a transplanting test bench is designed and built,and the kinematic characteristics and operating performance tests of the mechanism are carried out.The test results meet the design requirements,which verifies the correctness of the method proposed in this dissertation and the rationality of the mechanism design.