Study On Large Deflection Performan Of Compliant Continuum Manipulator

In recent years,much research forcus on the continuum manipulator.The continuum manipulator is composed of elastic and soft components,which has favorable flexibility and motion performance when it inspects in complex and narrow environment.However,the deformation of the continuum manipulator is extreme complex due to the non-linear of the elastic and soft components,especially the large deformation and the vibration during the moving.Also,the increasement of the scale of the continuum manipulator would leads to intensify its deformation and vibration seriouly.Therefore,this paper focuses on the basic deformation principle,large deformation behavior and vibration characteristics of the continuum manipulator.The specific research contents are as follows:(1)The global kinematic model of the posture transformation of the continuum manipulator is established.According to the assembly and driving form of the main elastic structure of the continuum manipulator,the deformation principle of its motion posture is analyzed.Further,based on the geometric form of the posture deformation,the global kinematics forward and inverse mapping relationship of the continuum manipulator is established divided into three levels of space,workspace,joint space and driving space.Then,according to the global kinematic model,the influence of key structural parameters on the workspace of the continuum manipulator is discussed.Finally,based on the proposed global kinematic model,the posture variation of the continuum manipulator when the free end of the manipulator realizes various tracks are simulated to verify its movement and deformation performance in theory.(2)The instantaneous kinematics model of the continuum manipulator is established,and the indexes of dexterity,manipulability and manipulability ellipsoid direction are proposed.According to the global kinematic model of the continuum manipulator,the differential equations of its instantaneous kinematics are obtained,and the Jacobian matrix is analyzed.Then,based on the influence of the condition number of Jacobian matrix on the precision of inverse solution,using the method of decomposing Jacobian matrix,the index of dexterity,manipulability and manipulability ellipsoid direction is proposed.Furthermore,the precision of continuum manipulator in different working areas and along different directions is analyzed.(3)A large deflection static model of the continuum manipulator is established.According to the structural form of the continuum manipulator,the idea that the continuum manipulator is equivalent to an equivalent beam is proposed.Then,based on the Euler-Bernoulli beam deformation theory and the elliptic integral solution principle,the large deflection behavior of the continuum manipulator under different load is analyzed,and the solution method is given.According to the static model,the numerical simulation of the continuum manipulator under the horizontal and vertical end loads is carried out,and the posture deformation behavior is analyzed.From the simulation results,the horizontal and vertical stiffness of the continuum manipulator are discussed.(4)The modal analysis method of the continuum manipulator is proposed,and the modal dynamic model of its vibration during the motion is established.Based on the Euler-Bernoulli beam motion theory,the fourth order motion differential equation of the continuum manipulator is derived,and the general solution form of its modal shape is obtained by using the specific boundary conditions,and also the modal frequency equation is established.Then,the modal response model of continuum manipulator under external excitation is calculated through the method of mass orthogonal and mode coordinate superposition.Further,kinematics model is transfer to polar coordinate system from Cartesian coordinate system.Finally,the dynamic performance of the continuum manipulator is analyzed based on the numerical model of dynamic response trajectory.(5)The proposed theoretical models of the continuum manipulator are verified by experimental analysis.The kinematic experimental results show that the motion accuracy of the flexible continuum manipulator is higher in the working area near the bending angle of 60~°,and higher in the direction of the ellipsoid axis,which is consistent with the theoretical regularity.The loaded deformation experiment shows that the theoretical large deflection static model could reflect the real deformation behavior of continuu manipulator prototype well when the load is less than 10N.In addition,through the loaded experiments,it is found that the stiffness of the flexible continuum manipulator in the horizontal direction is greater than that in the vertical direction.The results show that the modal characteristics calculated by the modal dynamic model proposed in this paper are consistent with the measured values of the physical prototype of the continuum manipulator,and can reflect the real-time track characteristics.