Analysis And Synthesis Of 2R1T Parallel Mechanisms Based On The Geometric Algebra

In the field of advanced manufacturing,such as aerospace,five-axis hybrid machine tool is an important equipment for processing the complex structural components with high efficiency and precision machining,in which the key part is the parallel mechanisms(PMs)with two rotational and one translational motion(2R1T).However,most of the existing 2R1T PMs have some problems,such as large number of single-DOF joints and virtual output rotational axes,which greatly affect the accuracy and stiffness of 2R1T PMs,and thus limit the practical applications.In order to solve the above problems,this dissertation uses the geometric algebra to design a type of novel 2R1T PMs with definite rotational axes and fewer number of joints.Meanwhile,this dissertation conducts performance evaluations and optimizations of 2R1T PMs,including the kinematics,stiffness and dynamics,and finally it is determined that the 2PRU-PSR PM is the best choice.In this dissertation,it is extended to the five-axis hybrid equipment,which is suitable for machining workpieces with complex structures.The main research contents and contributions of this dissertation are as follows:Using the geometric algebra as a mathematical tool,this dissertation focuses on the machining requirements of large aerospace structural components,and synthesizes a type of novel non-redundant actuated and redundant actuated 2R1T PMs with definite rotational axes.Many new 2R1T PMs are proposed,including the non-redundant actuated 2R1T PMs(Tex3 and 2PRU-UPR),and redundant actuated 2R1T PMs(Tex4,Hex4 and 2PRU-2UPR).Using the orthogonal complementary relation between motion space and constraint space in the geometric algebra,an analytical solution of the constraint and actuation wrenches of limbs in the PM is obtained.Using these analytical wrenches,this dissertation presents the kinematic performance evaluation and parameters optimization of some 2R1T PMs with definite rotational axes,including the non-redundant actuated2R1T PMs(Tex3 and 2PRU-UPR),and redundant actuated 2R1T PMs(Tex4,Hex4 and2PRU-2UPR).Using the framework of geometric algebra,a general method for the analytical elastostatic stiffness modeling of overconstrained PMs is proposed.Considering the compliances of limbs,the analytical elastostatic models and stiffness matrices of limbs and overall PM are established by using the strain energy,which have concise expressions and clear physical meanings.The elastostatic stiffness models of overconstrained PMs,Tex3 and Tex4,are developed and verified by using the proposed method.Under the framework of geometric algebra,a general method for the analytical inverse dynamics modeling of PMs is proposed.Firstly,the property of outer product in the geometric algebra is used to directly determine the intensities of velocities and accelerations of joints in the limbs of PMs.Then,the velocities and accelerations of links in the limbs can be calculated.Finally,combined with the principle of virtual work,the analytical expressions of values of actuated forces/torques of joints in the PMs can be obtained.Two PMs are selected to verify the correctness of proposed method.Meanwhile,the comparison with the natural orthogonal complement method based on the Newton-Euler equation is used to illustrate the calculation efficiency of this method.The 2PRU-PSR PM is selected and analyzed in detail,including the mobility,kinematics,elastostatic stiffness and inverse dynamics,and finally it is determined that the 2PRU-PSR PM is more suitable for machining workpieces with complex structures.This dissertation also carries out the design of prototype,and fabricates a prototype of five-axis hybrid machine tool based on the 2PRU-PSR PM.The prototype is controlled to achieve the five-axis machining of workpieces.This dissertation has an important reference for the design and analysis of 2R1T PMs with definite rotational axes,and is of great significance for promoting the innovation and engineering applications of parallel robot technology.