Stiffness And Dynamics Of 3-DOF Robot With Flexible Joints

Stiffness is one of the important considerations in the research and designof robot , for which affects performance of dynamics and orientationprecision.The paper focuses on the stiffness of the closed-loop mechanism of3-DOF with flexible joist and the parallel mechanism of 3-DOF with flexiblejoist.Firstly , it describes the closed-loop mechanism of 3-DOF with flexiblejoist and analyses the first-order influence coefficient, the second-orderinfluence coefficient, velocity and acceleration about this mechanism, withemphasizing stiffness on the static balance.On the base of the influencecoefficient stiffness matrix of this mechanism is deduced.Rayleigh quotient issolved with singularity value of the matrix.Else it presents stiffness adjudgingindex. Distributing of minimum singularity value of the stiffness matrix on theXY plane is protracted with the help of MATLAB program.Based on stiffnessmatrix, the paper discusses the direction stiffness of the mechanisms.It also selects the parameters relaying on the inverse kinematics solution ofthe parallel mechanism of 3-DOF with flexible joist.The mechanism issimulated with the selected parameters. It concludes the first-order and thesecond-order influence coefficient of the platform and every flexible joint.Andanalyses velocity and acceleration of those.Meanwhile it depicts the change ofthe curve on the XY plane.Static force equilibrium equation is established applyingkinematic-dynamic dual and the first-order influence coefficient.And staticbalance of the parallel mechanism of the 3-DOF with flexible joints isinvestigated.While in the given situation dive joints torques are illustrated in themapping.Based on the study about the closed-loop mechanism of 3-DOF withflexible joist and static analysis, the stiffness matrix with which characteristic ofthe parallel mechanism of the 3-DOF with flexible joints is examined with thefirst-order and the second-order influence coefficient.Depending on the rayleighquotient, it changes the matrix into numeric and plots the minimum singularityvalue of the stiffness matrix on a chart.At last, the paper studies the dynamic of the parallel mechanism of the3-DOF with flexible joints from the Newton-Euler formulation.Under aspecially situation it illustrates the mechanism drive force in the mapping withthe relation to position, velocity and acceleration of the platform.