Research On Kinematics And Stiffness Of 3-RPR Spherical Parallel Mechanism

Spherical parallel mechanism is a special kind of spatial parallel mechanism, whose range of motion of the moving platform’s reference point is on a fixed spherical surface. It not only has performance advantages of the parallel mechanism such as stiffness, high precision, but also has performance advantages such as large workspace, not ease interference and simple kinematics calculation. Based on the above characteristics, spherical parallel mechanism is mainly used in the minimally invasive surgery robot, rehabilitation robots, CNC machine tools and adjustment, positioning device in astronomical equipment.In this paper, the kinematics and stiffness of 3-RPR spherical parallel mechanism are studied. First, the configuration of the mechanism is analyzed based on the screw theory. The configuration rule of the symmetric three branched spherical parallel mechanism is analyzed through the relationship between the branch motion screw system of the parallel mechanism and the motion screw system of the moving platform. Then the configuration characteristics of the 3-RPR spherical parallel mechanism are derived by the evolution of the kinematic pair. The order of the spherical parallel mechanism is found to be three by using the screw theory. The Kutzbach-Grvbler formula is applied to the given model to verify that the degree of freedom is 3.Secondly, the kinematics of 3-RPR spherical parallel mechanism is studied. Through constraint equations established by use of the equivalent shaft angle principle and the coordinate transformation matrix, the inverse and forward position of the mechanism are obtained, the velocity, acceleration is further analyzed and the Jacobian matrix are obtained. Based on the inverse solution, the workspace is obtained by inverse solution and MATLAB programming. A new nonparametric method is proposed to make 3-RPR spherical parallel mechanism can realize a given arbitrary spherical trajectory.Then, the static and stiffness of 3-RPR spherical parallel mechanism are analyzed. In consideration of the moving platform deformation, by using the strain energy and cassette theorem, the flexibility matrix of the platform, a connecting rod, a motor in the mechanism are derived respectively, and the stiffness matrix of 3-RPR spherical parallel mechanism is sought out by lumping all to together and the Stiffness Evaluation Index KSI is put forward. Finally, through the finite element simulation analysis, it is concluded that the maximum stress and strain of the mechanism are in the limit position.Finally, the co-simulation of 3-RPR spherical parallel mechanism is conducted by using SolidWorks and Adams. The assembly model of the mechanism is established in SolidWorks and constraints are added in ADAMS. The virtual prototyping is established. The driving rules are obtained according to given trajectory based on inverse kinematics. Then the positive and inverse kinematics simulation are conducted.The dynamics of 3-RPR spherical parallel mechanism is simulated in two cases, the moving platform is subject to external force and is not subject to external force. The change rule of the driving power and moment are obtained.