Kinematics And Performance Analysis Of2PRU-(2PRR)U Parallel Manipulator

With the development of Parallel mechanism theory and technology, Parallel mechanismhas been widely applied in the field of industrial manufacturing. Imperfect DOF parallelmechanism has received much attention for the advantages of their simple structure, low cost andeasier to control than parallel mechanism with six degrees of freedom. In this background, thispaper presents a new1T2R parallel mechanism with three degrees of freedom and has carriedout the analysis on the kinematics and performance. The work is as follows:1) To analyze the DOF of2PRU-(2PRR) U parallel mechanism with screw theory, and findout that this mechanism has3DOF. To describe the position of mechanism’s moving platformwith u-v-w Euler Angle, and come to the conclusion that the angle γ comes from movingplatform rotating by axle W is always0. In total, the3parameters (Pz, θ, ψ) are used to describethe position of moving platform origin in this article.2) To list and solve the equations of mechanism’s position with geometric graph methodaccording to structure diagram of the mechanism. There are16solutions of the equations,12ofwhich are feasible solutions after excluding interferential solutions. In engineering applications,the optimal solution can be picked out according to the principle of minimum energyconsumption.3) To deduce the velocity mapping matrix (Jacobi) between parallel mechanism’s drivinginput and end effector’s output according to the principle that the velocities of rigid connectingrod’s two endpoints are the same. To analyze and calculate Jacobi matrix and obtain the positionsand characters of mechanism’s singular forms including2kinds of boundary singularities,1kindof local singularity and4kinds of structural singularities.4) To determine the biggest swing ability of moving platform according to the singularity ofmechanism. To analyze the interferences between paired U hinge joints and between pairedconnecting rods, and also the effects of driving slider’s maximum working range on the biggestswing ability of moving platform. Then to work out revised swing ability and searchmechanism’s work space in numerical search method with Matlab. After that, to draw therelevant chromatograms, which shows that the mechanism’s working space is a cylinder withupper and lower end faces in shape of part of spherical surface.5) Based on the assumption of the model and according to the principle of virtual work, thestatic stiffness of the mechanism and bearing capacity are deduced. According to the mappingrelationship of the driver’s input and the end of actuator’s output, the dexterity of PM is derived.By analyzing the calculation results of instance and the relevant atlas, we can get a conclusion which the performance of PM is better when working in the center position and it is poor whenworking in the singular form.6) Swinging ability of moving platform was identified according to the singularitycharacteristics of this parallel mechanism, the influence of U hinges in pair to the swing ability,interference between linkages and the working scope of driving slider to the workspace of thismechanism were analyzed. The workspace of this mechanism was drawn by using numericalsearch method based on MATLAB. Meanwhile, the static stiffness, dexterity and bearingcapacity of this parallel mechanism were analyzed and relevant atlases were drawn, whichprovide theoretical basis to parameter optimization of this mechanism.