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New Mechanical Generators of Schoenflies Motion Implementing Bennett Linkages

[+] Author Affiliations
Chung-Ching Lee

National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan

Jacques M. Hervé

Ecole Centrale des Arts et Manufactures, Chatenay-Malabry, France

Paper No. ESDA2012-82224, pp. 211-216; 6 pages
  • ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 3: Advanced Composite Materials and Processing; Robotics; Information Management and PLM; Design Engineering
  • Nantes, France, July 2–4, 2012
  • Conference Sponsors: International
  • ISBN: 978-0-7918-4486-1
  • Copyright © 2012 by ASME


Based on the Bennett 4R chain, we construct a rotating loop by fixing one R axis to the frame and the fixed R becomes a coaxial double R pair. The R pair opposite to the fixed double R is replaced by a spherical S pair which can be equivalent to a (RRR) open chain with non-coplanar intersecting axes. In the (RRR) sub-chain, we choose special axes and derive R|- R|(R(RRR)R chain moving with 2 DoFs. That moving R becomes a coaxial double R with the addition of another rigid body and the obtained chain with hybrid topology generates a 3-dof motion, which is mathematically modeled by a 3D submanifold of a 4D group of X motions. Because of the product closure in an X-motion group, adding an H pair with any pitch and an axis parallel to the fixed R axis leads to a mechanical generator of a 4D X-motion group. Then, parallel arrangement of two generators of the same X motion gives a new parallel generator of X motion, which can be actuated by four fixed R pairs; the two Hs must have distinct pitches. A special design with four collinear actuated axes is revealed too.

Copyright © 2012 by ASME
Topics: Linkages , Generators



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