Study Of Several Types Of Parallel Mechanism Using Screw Theory

The screw theory has many intersections in modern mathematics.As an important role in the field of institutional and robotics research,it has the characteristics of clear geometric concept,simple algebraic operation,many clear physical significance and so on,so it has become one of the mathematical foundations of institutional science and robotics.There are many advantages of parallel mechanism,such as: compact structure,small cumulative error and strong carrying capacity,etc.,widely used in many fields,such as: sports simulator,parallel machine tools.In view of this,this paper is based on the theory of spin to several parallel institutions on freedom and kinematic analysis.Two methods and principles of the degree of freedom analysis of parallel bodies are presented.They are also the most widely used two methods---G-K guidelines(including the revised G-K guidelines)and screw theory.The application of the theory of spin,the traditional G-K guidelines and the revised G-K guidelines provide many methods of degree of freedom analysis for parallel bodies.First,establish a global coordinate system to determine the motion-screw system for each branch,use the duality between constraint-screw system and motion-screw system to calculate the constraint-screw system for each branch,then get the constraint-screw multiset of the piatform.Use its maximum linear independent group to derive the platform motion-scerw system to determine the motion of the platform.Finally,it is judged whether there are redundant constraints,and the traditional G-K criteria and the revised G-K criteria are used to verify the correctness of the results.This paper successfully explores the kinematics of the 3-RPS parallel mechanism by using the theory of rotation,including the positive position of the agency's motion platform,positive inverse velocity,acceleration analysis and so on.First,the positive position analysis is carried out by Sylvester meta-method,and an unknown number of 16 polynomial expressions is obtained,so that all possible solutions to the initial analysis are calculated systematically.Then,the velocity and acceleration analysis is carried out by the theory of rotation.To do this,the speed and accochemical acceleration state of the moving platform relative to the fixed platform are expressed in the form of spins in three branches.Through the Klein form of Li algebra,the spatial mechanism of positive kinematics solution is derived simply and compactly by using the amount of inter-rotation.Expressions are simple,compact and can be easily converted into computer code.