Research And Application Of Kinematic Performance Of 3-PPR Spherical Parallel Mechanism

Three degree of freedom spherical parallel mechanism is an important branch of the few degrees of freedom parallel mechanism.The reference point of the moving platform moves on a spherical surface.Due to its special trajectory,it can be applied to the task with spherical surface,such as: high-precision spherical machining,aerospace positioning and mapping system and the combination of bionic joints and so on.In this paper,3-PPR spherical parallel mechanism is selected as the research object,and the kinematic characteristics of the mechanism are studied from the theoretical and numerical aspects.It provides theoretical basis for the development of 3-PPR spherical parallel mechanism.Firstly,the vector closed-loop equation is established using the structural features of 3-PPR spherical parallel mechanism.The position coordinates of the kinematic pairsof 3-PPRspherical parallel mechanism is calculated in the static coordinate system.The position vectors of the kinematic pairs are given.The kinematic spiral system of three limbs are written.The degree of freedom of the parallel mechanism is calculated.The inverse spiral system is compared and analyzed to verify the correctness of the calculation results.Secondly,on the basis of the kinematic spiral system of each limb,the spin matrix is used to establish the constraint sub-matrix and the motion matrix.Then,the Jacobian matrix is used to study the existence of the singularity of the constraints and the singularity of the motion,the discussion found that the body does not exist singularity.Thirdly,the factors influencing the work space of 3-PPR spherical parallel mechanism are analyzed.The range of influencing factors is given.Combining the positive solution equation of the kinematics,Monte Carlo method and Matlab programming are used to calculate,analyze the results.The singularities of the mechanism are verified.Fourthly,the direct method of the influence coefficient of the few-degree-of-freedom parallel mechanism is discussed.The first-order influence coefficient matrix and the second-order influence coefficient of 3-PPR spherical parallel mechanism are given using the kinematic spiral system matrix.The first-order influence coefficient matrix and the second-order influence coefficient matrix of the parallel mechanism are verified by numerical method and simulation method.The results of the two methods are compared and analyzed to verify the correctness of the influence coefficient matrix..Then,the simulation of the 3-PPR spherical parallel mechanism is carried out.By changing the setting of the driving function,the influence of the constant speed drive and the sinusoidal drive on the kinematics of the 3-PPR spherical parallel mechanism in different modes is compared and analyzed.Finally,based on the ankle movement characteristics and ankle rehabilitation mechanism,3-PPR spherical parallel mechanism is integrated.The trajectory at the ankle is planned.The appropriate driving mode is selected.The example is simulated and compared with the ankle movement characteristics and ankle rehabilitation mechanism to the requirements of the body.The feasibility of 3-PPR spherical parallel mechanism used in the ankle rehabilitation robotis proved.