Analysis Of Stiffness And Elastic Deformation For 4-DOF And 5-DOF Parallel Machamisms With 3 Legs

As a new thing of the mechanism, lower-mobility parallel mechanism has become more and more popular in the field of robotic research. With the rapid development of manufacturing industry, robots not only need to be lightweight but also should be more efficient in action. Some lower-mobility parallel mechanisms which have lightweight and slender-elastic arms have been commoditized. Stiffness is one of the most important performances of parallel machines in the early design stage as it determines the dynamic characteristic and positioning accuray of the robot. Therefor, it has very important theoretical and practical significance to study the stiffness properties of these lower-mobility parallel mechanisms with elastic arms.This paper analyzes a class of new type 4-DOF and 5-DOF parallel mechanisms with 3 legs. Constrained forces and elastic arms are the key of this study. Based on a new approach, the stiffness matrix could be built for both of 2SPS+UPR and 2SPS+PUPR parallel mechanisms. Then the terminal elastic deformation is obtained. At last, the analytical value is vertified through the finite element method.Through the analysis of the stress and deformation of the mechanism, branch stiffness matrix is built. The sign of matrix element is also analysized and discussed on the detailed. Based on the approach of vitual spatial kinematic pair, the relation on branch deformations and derminal deformations of this class of lower-mobility parallel mechanisms is built through solving the Jacobin matrix of the vitual mechanism. Then the terminal stiffness matrix is obtained.With the help of CAD variable geometry approach, simulative mechanisms of the original mechanism and the vitual mechanism are constructed. Afterwards, the Jacobin matrixes of them are vertified by their simulative mechanisms. Then with the initial condition of the pose of the teminal and under the effect of external forces and moments the theoretical curves of pose, constrained forces, branch deformations and terminal deformations are drawn in a certain period.Based on the finite element method and under the effect of external forces, equivalent stress, equivalent elastic strain, total deformation and directional deformation are solved. For one thing, the equivalent elastic strain is contrasted with the effect of the constrained forces in theory, for another thing, with the initial condition of the pose of the teminal and under the effect of external forces and moments the theoretical curves of the total defoamation and the directional deformation are compared with the curves of simulation values.