Research On Inverse Dynamics For The Planar 3-(?)RR Rigid-flexible Parallel Robot

With development of Chinese economy and upgrading of the structure of economic,the number of robots in manufacturing industry has rapidly increased.The flexible link studied in this paper inevitably undergoes large flexible deformation due to internal forces during rapid motion of parallel robots,which makes mechanical characteristics of robot different between rigid model.In this paper taking the deformation of light link as a precondition,the inverse dynamic model of rigid-flexible coupling system is described by absolute node coordinate method and natural coordinate method.The generalized-alpha method and Newton iteration method are used to solve the numerical problems in this paper.The mechanical characteristics of rigid-flexible model and rigid model have been also compared.In addition,the main tasks and findings of this paper are summarized below:(1)Inverse Kinematics and Inverse Dynamics Analysis of Planar 3-(?)RR Rigid Parallel Robot.The configuration of planar 3-(?)RR planar parallel robot is introduced.The joint angle,joint angular velocity and joint angular acceleration are analyzed by vector loop method.The simulation shows that the image of angular velocity and angular displacement has derivative relation and the image of angular acceleration and the angular velocity has derivative relations,which proves the correctness of the inverse kinematics model.According to Koenig's principle,the kinetic energy of the links and the moving platform has calculated respectively.Then the kinetic energy of the mechanism can be calculated.Based on the principle of rigid body size invariance,the constraint equation is established by using the radius of the outer circle of the moving platform.The inverse dynamic model is established based on Lagrange principle with Lagrange multiplier.Simulating mechanical properties of robots has based on MATLAB software.(2)Inverse Dynamics Analysis of Planar 3-(?)RR Rigid-flexible Coupling Parallel Robot.The mass matrix of rigid members is derived by using natural coordinate method.The shape function.is obtained by using undetermined coefficient method.The mass matrix of flexible link is derived by using shape function and absolute nodal coordinate method.The mass matrix of robot is assembled and inertial force also has derived.Generalized driving force based on virtual work principle is derived by equivalent couple of forces.Constraint equation based on the Principle of rigid body size invariance is set up by length of rigid link and size of platform.Binding force is derived by constraint equation.Inverse dynamic model of planar 3-(?)RR rigidflexible parallel robot can be constructed by adding elastic force and trajectory constraint equation.(3)Numerical Solution of Planar 3-(?)RR Rigid-flexible Coupling Inverse Dynamics Modeling.The strain energy reduced is split with reduced integration method to avoid Poisson locking and invariant matrix is used to improve the computing speed greatly.By the simulation with a circular trajectory of S-type acceleration and deceleration,the inverse dynamic model of the parallel robot is solved by generalized-alpha method,Newton iterative method and Rigid body correction method.The experimental iteration results satisfy the setting precision,maximum transverse deformation at the midpoint of the flexible beam is 4.701 mm.The change rule of shear angle at the midpoint of the flexible beam has symmetry,and the driving joint angular velocity is different from that of the rigid model.The change rule of driving joint variable is smooth.Therefore,the present modelling method with solution algorithm can be proved feasibly and using S-type acceleration and deceleration can be proved necessarily.It is great theoretical significance for control in the future.