Synthesis Analysis And Prototype Research On Parallel Mechanisms With Constant Jacobian Matrix

The Jacobian matrix of parallel mechanism(PM)represents the mapping relationship between velocity and force in joint space and operation space.It is the basis of mechanism analysis and design,performance evaluation and motion control.It is also one of the most important tools to characterize PM.The Jacobian matrix of most PMs varies with the pose of PM,resulting in the change of the performance parameters such as the motion and force of PM.If all elements of the Jacobian matrix can always remain constant under any pose in the whole workspace of PM,or some elements of the Jacobian matrix can always remain constant,the mapping relationship between velocity and force in joint space and the operation space becomes simple,and the strong coupling relationship between input motion of the actuated joints and output motion of the moving platform is weakened.The more constant elements in the Jacobian matrix,the easier the kinematic and dynamic analysis of PM,which brings many conveniences to the motion control,trajectory planning and real-time online control of PM.At the same time,it is of great significance to improve control accuracy and control efficiency of PM.Therefore,the PM with a constant Jacobian matrix will have good practical application value.In this paper,type synthesis and performance analysis of the PM with a constant Jacobian matrix,motion control and trajectory planning of the robot prototype based on the PM with a constant Jacobian matrix are studied.The research includes type synthesis of the PM with a completely constant Jacobian matrix,type synthesis of the PM with a partially constant Jacobian matrix,performance evaluation and comparative analysis of the PM with a completely/partially/non constant Jacobian matrix,development of robot prototype based on the PM with a constant Jacobian matrix,and its dynamic control and trajectory planning.These research works are not only the innovation and improvement of the theoretical research of the parallel mechanism with a constant Jacobian matrix,but also provide theoretical support and guidance for the development and application of the parallel robot with a constant Jacobian matrix.The main research contents of this paper are as follows:(1)The type synthesis theory of the PM with a completely constant Jacobian matrix is discussed.Based on the screw theory,the Jacobian matrix of PM is solved;Starting with the reciprocal product of the transmission wrench screw and the input twist screw,the criteria for completely constant Jacobian matrix of the translational PM,the rotational PM and the mixedmotion PM are discussed respectively,and the reason that the Jacobian matrix of the rotational PM and the mixed-motion PM cannot remain completely constant is analyzed;Based on the criteria,the principle of constrained screw synthesis and the reasonable selection theory of actuated joint,the configuration of translational PM with a completely constant Jacobian matrix is given.(2)The type synthesis method of the PM with a partially constant Jacobian matrix is studied.The method includes the limb construction and the combination of the limbs.In the process of limb construction,based on the basic types of planar sub-chains with three degrees of freedom(Do Fs),the way of realizing partial constancy of Jacobian matrix is discussed.Based on the principle of type synthesis of PM,four methods of constructing the transmission wrench screw with changing direction are expounded.In the process of the combination of the limbs,two sufficient conditions for constructing PM with a partially constant Jacobian matrix are proposed.Based on this condition,three,four and eight cases of limb combination of translational PM,rotational PM and mixed-motion PM are summarized,and the typical configurations of these PMs are given.Taking four typical PMs as examples,this paper expounds their construction process,analyzes the input velocity and force curve under the constant output of the corresponding PMs,and points out that the number of constant elements of Jacobian matrix is of great significance to improve the control accuracy and efficiency of PMs.(3)Taking 3-PPRU PM as the research object,the performance of the PM with a completely/partially/non constant Jacobian matrix is analyzed and compared.The singularity of the PM with three different Jacobian matrices is analyzed,as well as the velocity and dexterity,force and payload isotropy,deformation and stiffness isotropy.From the perspective of force transmission,the force transmission manipulability index(TMI)and force constraint consistency index(CCI)are put forward;The performance,important characteristics and application prospect of 3-PPRU PM under three different Jacobian matrices are summarized.(4)The dynamic control of 3-CRU parallel robot prototype with a constant Jacobian matrix is studied.Based on Lagrange method,a dynamic model of the robot including modeling errors and external disturbances is established;The dynamic parameters of the robot are identified based on the improved Fourier series and least square method;Based on the dynamic model,a feedforward torque sliding mode variable structure controller is designed;The 3-CRU parallel robot system is built,and the dynamic parameter identification experiment of the robot and the trajectory tracking experiment of the robot are carried out to verify the accuracy of the identification and the effectiveness of the algorithm.(5)The trajectory planning of 3-CRU parallel robot prototype with a constant Jacobian matrix is studied.A trajectory generation method based on Finite Impulse Response(FIR)filter is studied.This method can plan the total running time of the trajectory in advance while taking into account the smoothness of the trajectory;Based on the linear forward and inverse kinematics equations of the parallel robot,a trajectory planning simplification strategy is proposed.The biggest advantage of this strategy is that it can arbitrarily increase the interpolation period in Cartesian space without affecting the trajectory accuracy of the robot,and there is no need for a twice interpolation in joint space;Aiming at the problem that the residual vibration generated by the robot after the high-speed motion stops affects the positioning accuracy of the moving platform,firstly,the internal causes of the residual vibration of the 3-CRU parallel robot are analyzed,the modal parameters of the robot are identified,and the corresponding input shaper is designed;The acceleration planning method is proposed to compensate the delay caused by the input shaper;Through simulation,it is verified that the actuated joint trajectory smoothness and the trajectory accuracy after twice interpolation in joint space of 3-CRU parallel robot behave well.Through experiments,it is verified that the trajectory planning simplification strategy of the 3-CRU parallel robot is feasible and the vibration suppression algorithm is effective.