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1. Introduction
Parallel kinematic mechanisms (PKMs) [1, 2] are characterized by multi-closed-loop structure [3], which is distinctly different from the open-loop structure of the traditional mechanisms, namely, serial kinematic mechanisms (SKMs). This distinct structure makes the PKMs have the features of high rigidity, low moving inertia, high dynamic performance [4], and high accuracy potential at the expense of strong coupling in terms of kinematics. For such a reason, PKMs have been studied intensively by the researchers from both academia and industry [5]. Gough-Stewart platform [6] is the first proposed and also the most famous six-degree-of-freedom (DOF) parallel structure; it has been extensively investigated from then on. The PKMs’ unique merits mentioned above make them suitable for the application of machine tools, especially in processing parts with complicate and freeform surfaces. Some engineering practices also indicate that machine tools based on PKMs outperform those based on SKMs in surface finish and geometric accuracy when machining hardened materials [7]. In this field, some machine tools based on fully parallel mechanisms are developed, such as Variax [7], Hexapod [8], Metrom, and others. Variax and Hexapod are based on the Gough-Stewart platform, and both of them need six-axis computer numerical control (CNC) and have relatively small workspace, especially the limited rotational capacity. Metrom is based on a 5-DOF fully parallel mechanism, and its rotational capacity can achieve 90°. This is a great advantage in the field.
In comparison, machine tools based on hybrid mechanisms, which combine the advantages of both PKMs and SKMs, have been extensively applied in industry and gradually became the development trend of high-speed, high-accuracy, and high-flexibility machine tools. In the...