| With the progress of the information technology and the development of the global manufacturing techniques, enterprises require more efficient and lower cost machine tools by reason of enhancing their competitive ability. But conventional machine tools will encounter many difficulities which are hard to overcome in the future, for instance of high-speed machining (path speeds exceeding 50 m/min ) and high-efficient space curved surfaces machining as well as flexibility of machines. Thus, it is very important to explore and study kind of modern machines. Parallel kinematic mechanism (PKM) has notable features of reduced mass of moving parts and thus increased acceleration reserves, in addition to that, PKM allow the implementation of modular construction methods and a clear improvement in the quality of the machined surface. Moreover, the production costs of parallel kinematic machine tools are reduced by the fact that a large number of identical parts can be used. This paper conducts the discussion of "Stewart platform" and it's design variants, and presents the analysis of kinematics, dynamics and control system of the double-angular PKM and 6-slide PKM; with a kinematics, dynamics algorithm developed, the simulating solutions of the characteristics of PKM are respectively drawn. High-speed machining or cutting with lasers and plasma is the important advantages of modern machine tools, and that has formed main trend in the development of the machine tools. Parallel kinematic structure (mechanism) can meet satisfactorily the demands on high speed machining. This paper presents the analysis of comparison between the Stewart platform and 6-slide PKM, making a suggestion that 6-slide PKM has more perfect specific kinematic property and controllable peculiarity than Stewart platform. For example, the 6-slide PKM can employ the simple structure of strut-components and realize the combination of several machining means, and has the workspace which extends infinitely in theory, etc..General PKM has no analytic positive solutions, which mirrors in the analysis of kinematic and dynamic. Jacobian matrix can not be gained; when solving the problem with the digital algorithm of Gauss-elimination, the coefficient matrix of linear equations group is high degree illness. This paper employs the dynamic-static force principle to simplify the mathematical models, and employs the virtual-displacement principle and adopts the SOR digital algorism to extract the dynamical performances. The solutions extracted is coincidental with the practical situations. There're 12 variables in the homogeneous transformation matrix when which is expressed by orientation cosine vectors, and 6 of 12 variables are in relation to rotation transformation. In case that the homogeneous transformation matrix for moving platform is expressed by fixed-axis Euler angles, only is three variables with respect to rotation transformation needed, then the course of extracting solutions is simplified. Double-triangle model Stewart platform has analytic positive solutions as a result of adopting special structure of complex ball hinge. This paper discusses two types of structure of complex ball hinge.The errors of mechanism which include errors of manufacturing components, assembling and controlling and the errors caused by temperature growth and elastic deformation of forced components affect directly the processing precision of virtual-axis machine tools. This paper employs differentiation transformation and the method of differentiating completely homogeneous coordinate transformation to set up errors equations group, the discussion of the errors of double-triangle PKM is conducted. When the moving platform is in horizontal posture, the rank primary element Crout solution is employed and the analytic solutions of errors dispersion is extracted, the nonsingular coefficient matrix is also proved.
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