A Study Of Pivotal Technique Of Machining Complicated Surface By Parallel Machine Tool Based On CAD Variation Geometry Theory

Nowadays, parallel manipulator (PM) is becoming more and more popular in the field of robotic research. And parallel machine tool (PMT) is an important application in industry. PMT, as a new-style machine tool, complements the traditional NC machine tool perfectly. The research of the basal theory of PMT is a part of the area of PM and machine tool studies. With the development of the industry, PMTs are becoming more and more important in actual applications. A further study of the basal theory on the PMTs is needed. This paper starts with the key problems in the process of machining complicated surface which are unable to establish the analytic equations, the main contributions are as follows:Based on CAD variation geometry approach, the uniform model of machining a general complicated surface by parallel robots is founded to solve all the input driving parameters in the process. The 3-UPRR and the novel unsymmetrical 3-UPU PMs with 3 translation degrees of freedom (dofs), and the novel 5 dofs 3SPS+RRPU PMT with middle driving limb are proposed. Three paths of straight-line, spiral and special letter curves are adopted, and the constitution method is expounded. And the model for normal machining by a 5 dofs PMT 3SPS+RRPU is founded.CAD variation geometry approach is proposed to solve the kinematics of PMs. The Euler angles are introduced into the CAD variation geometry. Based on the finite-differential theory, a unified method is proposed for solving the position-orientation, linear velocity/ acceleration, and Euler angular velocity/ acceleration. A novel 5 dofs 2SPS+RRPRR PM with 3 limbs is put forward. Based on the 2SPS+RRPRR and the classical 3/6-SPS PMs, the accurate solutions of the kinematics are solved. It lays a theoretical foundation and provides a method for solving the velocity and acceleration in the process of machining a complicated surface.Based on the CAD variation geometry, the active forces and constrained forces of any PM are solved from two aspects of the principle of virtual work and the static balance equations. Three pivotal conclusions are induced and verified for the case of using the principle of virtual work. The first method is introduced with 3-RPS and 2SPS+2UPU PMs as examples; and the second method is explained with the 3UPUⅠPM containing only the constrained forces and 3UPUⅡPM containing only the constrained torques as examples.Synthesizing all the methods above, it is suggested that the CAD variation geometry should be introduced to solve the key problems in machining a surface. For the complicated surface which is hard to establish the math equations, the normal simulation machine system is constructed based on the 5-dof 4SPS+SPR PMT. All of the input parameters in the whole machining process are solved according to the expectant tool path and machining velocity. The kinematics and statics are analyzed in advance, and the singularity or the shape point of the kinematics is found. By modification of the kinematics parameters, these positions can be avoided and the machine quality can be ensured. The driving forces along the two paths are analyzed in order to choose an appropriate curve.The analytic model of the novel 5-dof 4SPS+SPR PMT is established, and the analytic equations for solving the velocity, acceleration and statics are derived. The 6×6 Jacobian matrix and Hessian matrix are obtained. The forward position of the PMT is analyzed, and it is claimed that the 5-dof PMT has 56 groups of solutions. The analytic solutions are validated by the CAD variation geometry approach.Based on the CAD variation geometry approach and the existing test-bed, a series of 3-dof 2SPS+UPU/SP PMs with the constrained leg are put forward. By analyzing the properties of their dofs, it is found that the 2SPS+UPU/SP PMs have two kinds of dofs: 3 translations; and 2 rotations plus 1 translation. Then the uniform analytic equations for solving the kinematics and statics are established. Taking the novel 2SPS+UPU/SP PM with the 2 rotations and 1 translation as the prototype, and based on the modularization test-bed of PM, the novel sample machine is exploited. Based on Windows Operating System and data collection by CAD variation geometry approach, the expectant track is painted by the sample machine in order to prove the validity of CAD variation geometry approach.