Theoritical Study Of A 5-Dof Parallel Manipulator Using A Rotational Driving And Four Translational Drivings

Nowadays, in the field of manipulators, parallel manipulators are widely used in various fields because of the advantages of high stiffness, low moving inertia and high compactness. Among them, limited-DOF parallel manipulators have broad application prospects, and gradually become the research hotspots in the field of parallel manipulators.In this paper, a 4SPU+RRPU 5-DOF parallel manipulator has been analyzed. The unified mathematical models of kinematics, statics and dynamics are established. And the workspace and singular position are also simply clarified.Three-dimensional entity of 4SPU+RRPU 5-DOF parallel manipulator is designed, and its inverse displacement is analyzed. The workspace of 4SPU+RRPU parallel manipulator is solved by CAD variation geometry method.Based on the constrained force/ moment of limited-DOF parallel manipulator, the kinematic mathematical model of 4SPU+RRPU 5-DOF parallel manipulator with a constrained force is established. The(6 × 6) Jacobian matrix and(6 × 6 × 6) Hessian matrix without partial derivatives are also derived. And the kinematic analysis is verified by CAD variation geometry method.Based on the principle of virtual work, static model of this parallel manipulator is established. By the constraint relations of 4SPU+RRPU 5-DOF parallel manipulator, equivalent mapping relationship between the angular velocities of the branches and velocity of moving platform is obtained. So this can complement the mathematical model of linear angular velocities of branches. Based on the principle of virtual work, unified dynamics model of 4SPU+RRPU parallel manipulator is established and the correctness is also verified.By the Jacobian matrix and the geometry method, the singular positions of 4SPU+RRPU parallel manipulator are analyzed. The results provided theoretical foundations to avoid the singular positions of this parallel manipulator for the application in the future.