Research On Kinematics Performance Of3-DOF Spherical Parallel Mechanism

As a special type of parallel mechanism, spherical parallel mechanisms not only have thecharacteristics of parallel mechanism, but also make up the elusive characteristics of parallelmechanism to some extent. Spherical parallel mechanism have many advantages whichinvolve compact structure, large work space, less possibility to occur interference betweenlinkages, easy to analyze its kinematic performance,easy to control and etc. It is widely usedin medical, aerospace, and robotics.In this paper, firstly, based on screw theory, this paper studied the type synthesis of thespatial parallel mechanism, abtained type synthesis of three-constraint kinematic chain, typesynthesis of two-constraint kinematic chain, type synthesis of one-constraint kinematic chainand type synthesis of zero-constraint kinematic chain. Through the3-RRR spherical parallelmechanism, verified the correctness of the spherical parallel mechanism type synthesisapproach, obtained the3-RRP spherical parallel mechanism. Then described the3-RRPspherical parallel mechanism and analyzed the freedom of the mechanisms, introduced therotation matrix and the equivalent angle-axis representation, established the inversekinematics model of the mechanism, induce the forward kinematics and inverse kinematicsanalysis, actuator velocity/acceleration and Jacobian.Secondly, based on the kinematic analysis, this paper studied the kinematicsperformances of the3-RRP spherical parallel manipulator.Through the Jocobian studied thesingularity of the mechanism, and obtained three possible singularities; through the principleof virtual work, drawn the relationship between the force and drive torque at the end of theactuator in the equilibrium state; With the concept of condition number, drawn the completelyisotropic conditions of the mechanism,that is complete symmetry; by adopting the search algorithm, the workspaces with different platform attitude angles and the projection in eachplane were obtained. The influencing factors for the size and shape of workspace wereanalyzed. These kinematics performances have a very significant impact on the sizecomprehensive and performance optimization.Then applied the functional principle and Newton-Euler establish the dynamic model,induced the dynamic equations, obtained the equation of driving torque, explained theinfluence of factors of driving torque. Finally, the paper studied the simulation of the sphericalmanipulator. By using UG/ADAMS software to verify the variation of displacement，theangular velocity and angular acceleration of the end effector of the mechanism reference point,proving the correctness of the modeling, further analyse the reference point of the end effectorwith force and no force, and changes in quality of the rod, obtained the variation of thedriving torque and driving power.The result of the theory and simulation of3-RRP spherical parallel mechanism in thispaper, laid a theoretical and practical basis for the research and application development onthe performance of other types of spherical parallel mechanism.