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Kinematic effects of number of legs in 6-DOF UPS parallel mechanisms

Published online by Cambridge University Press:  31 January 2017

Mohammad H. Abedinnasab*
Department of Biomedical Engineering, Rowan University, Glassboro, New Jersey 08028, USA
Farzam Farahmand
School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran; RCBTR, Tehran University of Medical Sciences, Tehran, Iran. E-mail:
Bahram Tarvirdizadeh
Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran. E-mail:
Hassan Zohoor
Center of Excellence in Design, Robotics, and Automation, Sharif University of Technology, Tehran, Iran; Academy of Sciences of I.R.Iran, Tehran, Iran. E-mail:
Jaime Gallardo-Alvarado
Department of Mechanical Engineering, Instituto Tecnológico de Celaya, TNM, 38010 Celaya, GTO, México. E-mail:
*Corresponding author. E-mail:


In this paper, we study the kinematic effects of number of legs in 6-DOF UPS parallel manipulators. A group of 3-, 4-, and 6-legged mechanisms are evaluated in terms of the kinematic performance indices, workspace, singular configurations, and forward kinematic solutions. Results show that the optimum number of legs varies due to priorities in kinematic measures in different applications. The non-symmetric Wide-Open mechanism enjoys the largest workspace, while the well-known Gough–Stewart (3–3) platform retains the highest dexterity. Especially, the redundantly actuated 4-legged mechanism has several important advantages over its non-redundant counterparts and different architectures of Gough–Stewart platform. It has dramatically less singular configurations, a higher manipulability, and at the same time less sensitivity. It is also shown that the forward kinematic problem has 40, 16, and 1 solution(s), respectively for the 6-, 3-, and the 4-legged mechanisms. Superior capabilities of the 4-legged mechanism make it a perfect candidate to be used in more challenging 6-DOF applications in assembly, manufacturing, biomedical, and space technologies.

Robotica , Volume 35 , Issue 12 , December 2017 , pp. 2257 - 2277
Copyright © Cambridge University Press 2017 

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