Terminal Constraint Analysis Of A Class Of 3+2 Type Limited-dof Serial-parallel Manipulators

The serial-parallel hybrid mechanism has advantages such as large workspace,strong stiffness performance,and good end flexibility,and has great potential for application in many fields.Among them,the properties of constraint/mobility of the end platform,as a fundamental problem in mechanics,are of great significance for the theoretical research and application of the limited-dof serial-parallel hybrid mechanisms.The project is based on the analysis method of terminal constrained screw,solving the constraint/mobility of a class of3+2 type limited-dof serial-parallel hybrid mechanism,and providing a relevant theoretical basis for subsequent research.Firstly,this paper introduces the correlation theory of the screw system,analyzes the principle of the terminal constraint/mobility of composition of the double-layer serialparallel hybrid mechanism based on this,and provides the corresponding formula for calculating the degree of freedom.Secondly,the article studied three types of 3+2 limited-dof series-parallel hybrid mechanisms:(3-PRS)+(2-RPS+SR),(3-RPS)+(2-RCR),and(UPR+UPU+UPS)+(UPR+RPU).The number of DOF of the end platform under different configurations was analyzed,and the properties of terminal constraints/motion screws were solved using geometric methods,further expanding the application scope of geometric method in solving the intersection of two screw systems in analytical geometric space.In order to verify the correctness of this method,this paper gives two numerical examples under different configurations for three hybrid mechanisms respectively,analyzes the quadratic surface and line cluster equations corresponding to the two sub constraint screw systems,and obtains the correct terminal constraint screw of the hybrid mechanisms.In addition,in order to reflect the advantages of intuitive geometric expression,this paper also gives the quadratic surfaces drawn by Matlab.In summary,this work has improved the relevant theory of double-layer limited-dof hybrid mechanisms and expanded the geometric analysis methods for analyzing the terminal constraints of such mechanisms.Finally,a double-layer hybrid prototype of(UPR+UPU+UPS)+(UPR+RPU)was built,and the prototype was debugged and applied through Solid Works and control systems.