Determination of particular singular configurations of Stewart platform type of fixator by the stereographic projection method
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, vol.29, no.13, pp.2925-2943, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 29 Issue: 13
- Publication Date: 2021
- Doi Number: 10.1080/17415977.2021.1960325
- Journal Name: INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.2925-2943
- Keywords: Hexapod fixator, singular states, stereographic projection, determination of characteristic values, two lines intersecting five rods
- Dokuz Eylül University Affiliated: Yes
Abstract
Hexapod-type external fixators based on a general 6-6 Stewart platform structure are extensively used to manage orthopaedic disorders. While implementing these robotic devices, a practical visual aid is needed to quickly identify their uncontrollable states referred to as singularities. Thus, a visible correlation between the singularity of hexapod-type external fixators and their particular configurations has been explored geometrically in this work. A novel method called stereographic projection is utilized for that purpose. A mathematical procedure has been established to determine the characteristic values of the singular states. It is found that in case four- out of six-rod directions intersect each other at a common point, two different singular robot configurations result. Besides, if four joint angles at the top and bottom rings of the hexapod are equal, rings being parallel, then five-rod directions are intersected by two lines each passing through the end joints of the fifth rod.