Orientation workspace verification for parallel kinematic machines with constant leg length. Verifikation eines Orientierungsarbeitsplatzes für parallelkinematische Maschinen mit konstanter Beinlänge

摘要

Compared to serial robots, parallel kinematic machines (PKM) offer superior properties. However, modelling and analysis of PKMs are challenging tasks due to their complicated kinematic structure. In this paper methods are presented to analyze the workspace of a class of 6 degree-of-freedom (dof) PKMs with constant leg length. These methods apply interval analysis in order to calculate the orientation workspace and to verify if a certain machine covers a desired workspace. The machines are assembled from a construction kit that defines components like legs, frames, and platforms. In this paper algorithms are presented to calculate and to validate the workspace of parallel kinematic machines with constant leg length. Due to the application of interval analysis the validity of the results is guaranteed. Equations have been introduced that take into account the link interference and the limits on both articulated and passive joints. The algorithms supply orientation workspace calculation and verification at a short runtime. Therefore, it is capable for the optimization of the parameters of the Linapod which requires a large number of function evaluations