Estimating the Controllable Workspace of Tendon-based Stewart Platforms

The controllable workspace of a tendon-based Stewart Platform is the set of postures where forces and torques at the end-eeector can be controlled. A necessary and suucient condition is given for those postures where forces can be controlled; thus, a superset of the controllable workspace can be calculated easily. External forces are modeled as an additional tendon xed at iniinity by introducing an unusual compactiication of IR n that contains one innnitely distant point for each direction. Tendon-based Stewart Platforms 1 are Stewart Platforms where the legs are replaced by tendons (Ming and Higuchi, 1994). They combine the advantages of classical Stewart Platforms with those of tendon-driven serial manipulators, in particular: very low structure weight, hence very low energy consumption, while maintaining relatively high rigidity and accuracy. Therefore, they can be used when high loads have to be moved with precision , e. g. in shipbuilding (Dagalakis et al., 1989), or when small loads have to be moved with high acceleration (Kawai et al., 1995). Their main drawback is the rather small workspace, so one of the key issues in research is calculating the workspace in order to optimize it (Jeong et al., 1999; Landsberger and Shanmugasundram, 1992). A detailed introduction to this problem is provided in (Verhoeven et al., 1998); here we just summarize some results. While the workspace of serial manipulators is deened as the set of postures that can be reached without violating geometrical constraints and 1 We write \tendon-based" instead of \tendon-driven" because the latter may be confused with Stewart Platforms with rigid links having tendons for transmission only.