Singularity-free spheres in the position and orientation workspaces of Stewart platform manipulators
Autor: | Anirban Nag, Sandipan Bandyopadhyay |
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Rok vydání: | 2021 |
Předmět: |
0209 industrial biotechnology
Polynomial Computer science Orientation (computer vision) Mechanical Engineering Computation Bioengineering Stewart platform 02 engineering and technology Workspace Computer Science Applications 020303 mechanical engineering & transports 020901 industrial engineering & automation 0203 mechanical engineering Mechanics of Materials Position (vector) Metric (mathematics) Algebraic number Algorithm |
Zdroj: | Mechanism and Machine Theory. 155:104041 |
ISSN: | 0094-114X |
DOI: | 10.1016/j.mechmachtheory.2020.104041 |
Popis: | This paper presents the computation of singularity-free regions in the position and orientation workspaces of Stewart platform manipulators (SPMs). Notwithstanding several previous publications in this regard, certain issues persist, such as the unavailability of analytical solutions and the consequent lack of accurate estimates of the numbers of solutions in various cases; the improper use of an incompatible metric while finding such regions inside SO ( 3 ) or SE ( 3 ) . In this paper, the singularity-free regions have been envisaged as spheres in either R 3 or SO ( 3 ) . An analytical formulation for identifying such singularity-free spheres (SFSs) is presented. Several algebraic methods are explored to solve the resulting set of polynomial equations, leading to valuable insights into the numbers of (finite, complex) solutions to this problem, in both the position and the orientation workspaces. A physically meaningful and mathematically sound metric is used while computing the SFS in the orientation workspace. The formulation and computational algorithms have been demonstrated by identifying the SFSs (in R 3 as well as SO ( 3 ) ) for multiple architectures of the SPM through implementations in the C language. |
Databáze: | OpenAIRE |
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