Optimization Analysis Method Of Parallel Manipulator Kinematic Model

The primary objective of this dissertation is to build a new algorithm that simplifies the resolution of the kinematic problems for all types of parallel robots without limiting the number of degrees of freedom.This algorithm applies to various parallel robotic structures in a general order with high accuracy and reliability,shorter execution time,easier to use than current methods.To this end,the numerical simulation and experiment results of parallel Scara robots prove that the proposed method can be applied to solve kinematic problems for a variety of parallel robots regardless of its structures and degree of freedom with several advantages such as shorter computation time,high precision,high reliability and rapid convergence of results.In addition,this dissertation also extends the application of the proposed method in the field of robot tolerance design.Two examples are used to verify the feasibility of the proposed method;the accuracy and efficiency of the proposed method for generating tolerance allocations are also illustrated by calculations and simulation results.Firstly,based on optimal problem applied on the robot arm the dissertation proposes a new approach to find kinematic parameters by transforming the kinematic problem of the traditional parallel robot into a nonlinear optimization with the objective function Rosenbrock-Banana.Through many tests,the best algorithm for the Rosenbrock-Banana function in the optimal problem is the General Reduced Gradient(GRG)method.Direct recovery of the kinematic control resulting from the optimal problem will reduce the preparation time of the programmable data.Secondly,classification of a parallel robot based on texture with or without prismatic joints,the dissertation has been grouped into three types of parallel robots:the non-prismatic parallel robot(type 1)and the prismatic parallel robots including the parallel robot with the active prismatic joints connected to its base(type 2),the parallel robot with the second prismatic joints from its base(type 3).The dissertation presented modeling for all types of parallel robot structures and how to convert the mathematical model of the kinematic problem of the parallel robot to the optimal form.The situations that may arise when applying the proposed method on the three types of parallel robots are fully argued.With type 1 of parallel robot,the initial mathematical models when transforming into optimal problem,the object function is the quadratic function,so directly apply the GRG to solve the kinematic problem but the initial mathematical models of type 2 and type 3 robots are the quaternary function,which is incompatible with the proposed method.Thus,the dissertation proposes to solve this problem by using the equivalent substitution configuration to downgrade the object function form of the two types of robots(type 2 and type 3)from quaternary function to quadratic function,which is compatible with the proposed method.Thirdly,the Microsoft-Excel solver application supports mathematical resolution,to illustrate the example,by solving the kinematic problem of the robot for some typical parallel robots for each type of robot are presented in detail.The assurance of a unique solution between two different spaces(joint space and work space)has been fully argued.The results of the reliability and precision tests showed that the proposed method was very reliable and accurate.By comparing with other algorithms to solve an optimal problem,which are Sequential Quadratic Programming and the Genetic Algorithm to solve the optimal kinematic problem,the proposed method has exceeded the accuracy(approximately from 10~2 to 10~4times)and has shorter execution time.Fourthly,the results of the inverse kinematic problem are used as information to control the trajectory of the robot in real time,presented in detail and illustrated by the Adams simulation software as well as experiments in the Scara parallel robot.Experimental results demonstrated the capability,accuracy and feasibility of the proposed method when applied to robot control in practice.Finally,in addition to solving the kinematic problem of the parallel robot,the dissertation also developed a new application of the method proposed in the field of the manufacture of robots in order to design the tolerances of the components(links and joints)to ensure the given accuracy of the end effector and vice versa.This technique applies not only to parallel robots but also to the robot arm.Two examples are used to verify the feasibility of the above method and the calculated result that the method can produce tolerance allocations accurately and efficiently.