Determination of particular singular configurations of Stewart platform type of fixator by the stereographic projection method

DÖNMEZ D., AKÇALI İ. D., AVŞAR E., AYDIN A., Mutlu H.

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, cilt.29, sa.13, ss.2925-2943, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 13
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/17415977.2021.1960325
  • Dergi Adı: INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.2925-2943
  • Anahtar Kelimeler: Hexapod fixator, singular states, stereographic projection, determination of characteristic values, two lines intersecting five rods, ROBOT, ELIMINATION, KINEMATICS, MECHANISM, DESIGN
  • Çukurova Üniversitesi Adresli: Evet

Özet

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.