The Second Order Theoretical Modeling And Experimental Research Of Flexible Manipulator Based On The Moving Boundary

As is known to all, the traditional rigid member has a very large volume and its material waste is serious, therefor the flexible member has become an important subject of research at home and abroad. Some research results of theory modeling has been obtained in the aspects which include the boundary condition of the flexible arm and deformation theory at home and abroad. But the research on modeling accuracy of flexible manipulator is very poor. The precise modeling is mainly embodied in three aspects compared with traditional modeling: Firstly, in traditional theory modeling, the modeling generally choose the first order linear simplified model, however the paper choose the second order nonlinear complex models; Secondly, the traditional modeling think dynamic boundary conditions of experiment is the cantilever boundary, so that cantilever boundary is chosen to theoretical modeling, however this paper holds that the dynamic boundary conditions of the experiment is not only a cantilever boundary, but four kinds of boundary conditions of the coupling. Therefore the paper choose four kinds of dynamic boundary conditions for theoretical modeling respectively, so as to find a real dynamic model that can accurately describe experimental conditions; Thirdly, the traditional classical deformation is generally selected to model for dynamic equation, However the model of the paper are discussed on the three kinds of deformation theory(classical deformation, the secondary deformation, integrated deformation). The accuracy of theoretical modeling of flexible manipulator is discussed from two aspects of theory and experiment in this paper based on the above three aspects.Firstly, In terms of theory modeling, the dynamics of flexible mechanical system are briefly introduced, including the introduction of space coordinates description of flexible mechanical system, the Lagrange dynamics equation of flexible mechanical arm, the theoretical derivation of mode shape function and the main vibration mode function and the modal frequency of a variety of dynamic boundary conditions, etc. The theoretical derivation was gained for single-link, two-link flexible manipulator through the Hamilton principle and Lagrange dynamic equation. Euler Bernoulli beam model is selected to model, considering the elastic deformation and dynamic boundary conditions of the main influence factors to establish the mathematical model of flexible manipulator at the same time. the free vibration displacement of each kind of model under the condition of the flexible arm was calculated through the theoretical numerical method.Secondly, in experiment, design the mechanical system, control system, driving system and test system of flexible arm, and set up the experimental platform of flexible manipulator based on the movement control CARDS. The inverse dynamics trajectory planning of the servo motor was designed, to make sure the actual input trajectory of the motor to keep close to theoretical input trajectory as far as possible by using PD control. The free vibration displacement data was sampled by experimental monitoring system and was processed by Digital filter.Finally, the comparative analysis was carried on considering dynamic boundary conditions and three types of deformation theory through the theoretical modeling of Flexible manipulate. The results indicate that three kinds of deformation theory has a little impact on free-tip vibration displacement For flexible manipulator in a certain dynamic boundary conditions. It also shows that dynamic boundary conditions has great effect on the vibration amplitude of flexible manipulator from Longitudinal and different dynamic boundary conditions has a great influence on modal frequency for the dynamics equation derived from the theory. the paper choose modal frequency of dynamics equation as the research object to validate the experiment model based on the theoretical modeling analysis and considering the existing experimental conditions. the vibration displacement at the free end of a flexible manipulator of theoretical model to calculate and experimental measurement were compared and analysis. The result reveal that the cantilever boundary is suitable to formulate the real situation for a single joint flexible mechanical arm model. But for double joints, it reveals an different result that the boundary conditions of the rotating flexible beam locate between that of cantilever-free and Hinged-free models, which coincides with the experimental results. The priority choice of boundary conditions is very clear in the theoretical modeling, which provides theoretical basis for precise positioning and actual application of the flexible manipulator.