Underactuated Control Of Planar Three Joint Robot With Flexible Arm

Flexible underactuated robot has the characteristics of flexible robot and underactuated robot,which adapts to the requirements of high speed and low energy consumption.This topic is the use of a planar 3R flexible underactuated manipulator,dynamic equations of the system are established using the flexible beam model is more optimized,and the dynamic simulation study of dynamical characteristics analysis of coupling joint.The main work is as follows:(1)In order to establish the accurate dynamic equation of the system,this paper studies how to choose the beam model which is more suitable for the flexible manipulator under the condition of complex stress.In this paper,the complex stress conditions at the two ends of the flexible manipulator are converted into shear and bending moment boundary conditions.(2)Through the joint simulation of ANSYS and ADAMS,for the manipulator model modal analysis modal of ADAMS model based on the results of the analysis,combined with the boundary conditions of the flexible beam mode,we choose the suitable boundary conditions to represent changes of flexible arm mode.The iterative calculation method for the boundary condition of the flexible beam is presented.Based on the analysis of the modal frequency of the two link flexible manipulator,the correctness of the iterative method is verified,which provides a more effective method to establish the dynamic equation of the system using the assumed mode method.(3)Using the flexible beam model with higher accuracy,the dynamic equation of the planar 3R flexible underactuated manipulator is established by the assumed mode method.Taking into account the motor fixing frame rigidity than the flexible part,in order to make the equation more accord with the real situation,and to facilitate the simulation,so the flexible manipulator as coupling component.Because the dynamic equations include generalized variables and modal generalized variables,the solution is more complex.Based on the derivation of the second kind of Lagrange equation,this paper presents a method to solve the various elements in the dynamic matrix.(4)Based on the dynamic model of the system,the acceleration coupling index.Compared with the ideal cantilever beam and simply supported beam model,the optimization of the flexible beam model can better reflect the acceleration coupling of free joints.At last,the coupling index analysis of the flexible underactuated manipulator and rigid underactuated manipulator is carried out.It is found that the free joint of the flexible underactuated manipulator contains more complex coupling conditions.Finally,the coupling analysis results show that the control of the elastic vibration of the flexible manipulator is the key to the system control,and provides the basis for the selection of the control scheme of the whole system.