Theoretical Analysis And Application Study Of Active Over-constraint Parallel Mechanisms Based On The Overall Jacobian Matrix

The research of the active over-constraint parallel mechenism is a frontier research in the field of robotics both at home and abroad.Compared with the general parallel mechanism,the essence of the active over-constraint parallel mechaim is the existence of the active over-constraint force/torque,which doesn`t influence the degree of freedom of the mechanism.Therefore,the kinematic performance and dynamic performance will be improved by active over-constraint.In this article,the different performance of the different mechanism has been analyzed,which is illustrated the influence of the active over-constraint on the mechanism.Firstly,the isotropic analysis of line vector force is presented in this article,which shows that the isotropic condition can be satisfied when the line vector forces is evenly distributed on a conical surface which cone-top angle is 109.472°.In addition,a novel type synthesis method of 3-dof translational active over-constraint parallel manupilators considering the isotropic of line vector force is put forward,in which the lay out of actuators is taken into acount as well.The 4-PRRR active over-constraint parallel manipulator is set as an example to illustrated the type synthesis method,to concluded that the istropic of load bearing capacity of the mechanism can be satisfied during its movement,which verify the isotropic analysis and the synthesis method that disscused above.The overall jacobian matrix of a general active over-constraint parallel mechanism is derived using reciprocal screw theory,which include the actuation jacobian matrix,constraint jacobian matrix and active over-constraint jacobian matrix.And the physical meaning of the row of the jacobbian matrix is presented.The 5-U(?)S/(?)RPU active over-constraint parellel mechanism is used to illustrate the method,and the mapping relationship of the velocity of the operating space and the working space is derived;the kinematic model of the 4-PRRR active over-constraint parallel mechanism is established,and the mapping relationship of the velocity and acceleration of the operating space and the working space are derived,the workspace of the mechanism is achieved as well.By taking into account the deformation of the supporting limbs,the expression equation of the internal forces of the mechanism is derived by combining the pseudo-inverse method and principle of virtual work.Secondly,the relationship between the internal force and the adjustable coefficient of each supporting limb is established;the independence of the adjustable coefficient of the active over-constraint limb is verified by decomposition of the idempotent matrix,so that the internal force can be coordinated by changing the stiffness of the active over-constraint limb.At last,the 7-S(?)S PM and 5-U(?)S/(?)RPU PM are investigated as examples,the relationship between the active over-constraint stiffness and internal force distribution are presented,which verifies that it is allowed to coordinate the internal force of each driving force by altering the proper stiffness of the active over-constraint actuator.Based on the jacobian matrix of the actuation and constraint,the stiffness model of the general active over-constraint parallel mechanism is derived.The stiffness model is further validated by experimental data.Moreover,the global stiffness matrix of the general active over-constraint parallel mechanism can be separated into two parts via matrix decomposition.The first part is the stiffness matrix of the corresponding non-active over-constraint parallel mechanism,and the second part is the stiffness matrix of the active over-constraint limbs(actuators).The 5-U(?)S/(?)RPU active over-constraint parallel machine tool(PMT)is used to illustrate this method.The PMT comprehensively reveals the effect of the elastic deformation of active-passive joints and some basic transmission parts.The different stiffness characteristics of the machine tool and its corresponding nonactive over-constraint 5-U(?)S/(?)RPU PMT are compared.Actuation redundancy is found to improve the stiffness performance of the machine tool efficiently.The elastodynamic model of the 5-U(?)S/(?)RPU active over-constraint PMT(parallel machine tool)is derived by combining the finite element model and substructure synthesis techniques in this paper.Firstly,the overall system is divided into different substructures.According to the theory of spatial beam element,the dynamic equation of the spatial beam element is derived,and then according to the dynamic constraint and kinematic constraint between the moving platform and each driving limbs,the dynamic equation of the overall system can be obtained by assembling the dynamic equation of the driving limbs.The dynamic response of the 5-U(?)S/(?)RPU active over-constraint PMT is analyzed.The control system of the 5-U(?)S/(?)RPU active over-constraint PMT is introduced,and a novel compliant actuator is put forward to adjust the structure of the PMT.Based on the compliant actuator,a homing strategy is put forward;a novel force/position hyprid control strategy is put forward,and the method is verified by experiment.