Continuous workspace analysis for parallel cable-driven Stewart-Gough platforms

Parallel cable-driven Stewart-Gough platforms consist of a end-effector which is connected to the machine frame by motor driven cables. Since cables can transmit only tension forces, at least m = n + 1 cables are needed to tense a system having n degrees-of-freedom. This results in a kinematical redundancy and leads to a (m – n)-dimensional solution space for the cable force distribution. For this reason, performing a workspace analysis requires advanced methods and is time consuming. However, reliable and robust algorithms are demanded to calculate the workspace for a given parameter set (winch positions and platform anchor points). Discrete methods are widely used to analyze the workspace. Singularities as well as cable collisions inside the workspace of a cable-driven Stewart-Gough platform are possible [1]. Therefore discrete methods may deliver wrong results due to the fact that intermediate points on the discrete calculation grids are neglected. In this paper, another approach is presented. The use of intervals avoids the problems described above and leads to reliable results. In the following the basic ideas of this continuous workspace analysis are shown. For practical application, e.g. in robotics, even more important is the parameter synthesis, i.d. the process of designing a robot for a predefined workspace. However, the workspace geometries are very complex and not intuitive in general. Here, the analysis methods are also extended for synthesis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)