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On the Mobility of Single Loop N-Bar Linkage With One Prismatic Joint

[+] Author Affiliations
W. Z. Guo, J. X. Wang

Shanghai Jiao Tong University, Shanghai, China

R. Du

Chinese University of Hong Kong, Hong Kong, China

Paper No. DETC2005-84910, pp. 1047-1055; 9 pages
  • ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B
  • Long Beach, California, USA, September 24–28, 2005
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4744-6 | eISBN: 0-7918-3766-1
  • Copyright © 2005 by ASME


Single loop N-bar linkages that contain one prismatic joint are common in engineering. This paper presents a systematical study on the mobility of this type of mechanism. It is found that this type of mechanisms can be divided into three categories: Class I, Class II and Class III. For each category, the slide reachable range is cut into different regions: Grashofian region, non-Grashofian region and change-point region. At each region, the rotation range of the revolute joint or rotatability of the linkage is able to determine based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. For active prismatic joint, the input revolute joint(s) is/are dependent in non-Grashofian region but independent in other regions. For passive prismatic joint, the revolvability of input revolute joints is dependent on the offset distance of the prismatic joint. Two special cases are illustrated with four and five bars. Examples are given to demonstrate the presented method able to cover all the cases of N-bar linkages with one or a set of adjoined prismatic joints and N-bar open-loop robotic mechanisms.

Copyright © 2005 by ASME
Topics: Linkages



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