Research On The Mechanism Analysis And Trajectory Planning Method Of Parallel Robots

Parallel robot has attracted more and more attention because of its high stiffness,large load and small accumulated error.This present work is focused on the mechanism performance and trajectory planning analysis methods of parallel robots.The methodologies of the research can be applied for kinematics/dynamics analysis,performance evaluation and trajectory planning of parallel robots.The contributions obtained in the full text are listed as follows:The improved homotopy continuation method is proposed for the position analysis of parallel robots in this dissertation.The closed-loop vector method is employed to intuitively solve the inverse kinematics of a parallel robot,and a trigonometric polynomial system equation system which is proved to be in deficit is obtained.Aiming at this type of deficit system,a new and improved homotopy continuation numerical method with a high-order iteration as the correction step is illustrated at the present work.Furthermore,the BKK bound is calculated as the upper estimation of the solutions,and an approximate starting system without increasing the scale of the problem is built to overcome the weakness that the traditional numerical method's dependence on the initial guesses.Based on the knowledge of Euclidean group SE(3)and Lie algebra,the rigid body dynamic model of translate 3UPU parallel robot is established by using the reciprocal screw theory and the virtual work principle.For the further study,a matrix form of the inverse/forward acceleration is deduced by using the method of constructing quadratic form cleverly.And this can lay a foundation for the analysis of performance evaluation indices in the next chapter.Based on the theory of error analysis,the first-and second-order performance evaluation indices,such as the global dexterity index,the fluctuation of the global dexterity index,the acceleration transmission efficiency index and the fluctuation of the acceleration transmission efficiency index are established in this dissertation.What's more,the obtained indices above are carried out for the scale analysis and synthesis of parallel robot.Faced with the complex problem of the parallel robot's workspace,a new mesh algorithm based on the knowledge of computer graphics is designed at the present work.Meanwhile the mesh algorithm is encapsulated into a program black-box which is embedded in a multi-objective optimization model.Therein,the multi-objective optimization model is with the maximum reachable workspace volume,the maximum global dexterity index and the minimum fluctuation of the global dexterity index as the objective function.Finally,the nondominant sorted generic algorithm-2 is utilized to solve the proposed multi-objective optimization model,and several groups of typical Pareto frontier solutions are obtained,which can be used as a reference for engineering project design.As in the case of the null acceleration at the initial moment of the typical harmonic trajectory and velocity trapezoidal trajectory,the element trajectories combination methods are used to improve them.In the dissertation,several element trajectories are introduced.Then,the combination of cycloidal trajectory and harmonic trajectory is used to improve the original cycloidal trajectory with the defect that the acceleration is not zero at the initial moment.At the same case,the combination of cycloidal trajectory and cubic polynomial interpolation trajectory is used to improve the original trapezoidal trajectory with the same defect above.The numerical results listed show that the acceleration curve is smoother than before and the improvement effect is obvious.