This paper compares three different methods for computing the determinant of a univariate polynomial matrix. From a systematic empirical study involving 100 trials of each numerical experiment, it appears that the method of FFT-IFT-based interpolation and evaluation performs the best in terms of both speed and accuracy of computation. The utility of this method is further demonstrated by a successful application to the classical problem of forward kinematics (FKP) of the general Stewart-Gough platform manipulator (SPM).
Identification of the safe working zone (SWZ) of a parallel manipulator can be an important part of its path-planning process or design. Computationally efficient and accurate methods are required to make these demanding calculations practically feasible. This paper looks at the Cartesian and polar variants of a 2-D numerical scanner which are applicable for 3-degrees-of-freedom (DoF) planar or spatial parallel manipulators and presents a detailed analysis of their relative speeds, advantages and disadvantages, based on a case study involving the spatial 3-RRS manipulator. Results of such a study provide the analysts with a deeper understanding of the functioning of the scanner, which in turn, helps the computation of the SWZ of other manipulators in a fast and reliable manner.Keywords Parallel manipulator • Safe working zone (SWZ) • Numerical scanning 1 Obstacles inside the SWZ are not considered in this case.
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