A generic force-closure analysis algorithm for cable-driven parallel manipulators Wen Bin Lim a, ⁎, Guilin Yang b , Song Huat Yeo a , Shabbir Kurbanhusen Mustafa b a School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 637098, Singapore b Mechatronics Group, Singapore Institute of Manufacturing Technology, Singapore 638075, Singapore article info abstract Article history: Received 21 June 2010 Received in revised form 7 April 2011 Accepted 8 April 2011 Available online 4 May 2011 Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. Due to the unilateral driving property of cables, the cables in a CDPM must always maintain positive tension. In this paper, a methodology based on convex analysis is developed for the force-closure analysis of fully-constrained CDPMs. This method is systematic, easy to implement and satisfies both the necessary and sufficient conditions. The key point of this method is to define a critical vector that must be positively expressed by the tension vectors associated with the driving cables. The solution can be found by resolving a limited set of linear equations. Following the same approach, the method is also extended to generate the static workspace for under-constrained CDPMs. Therefore, this generic force-closure analysis can cater to the workspace analysis of both fully-constrained and under-constrained CDPMs. The computationally efficiency of the algorithm is verified through simulations. © 2011 Elsevier Ltd. All rights reserved. Keywords: Workspace analysis Cable-driven parallel manipulator Force-closure analysis 1. Introduction A cable-driven parallel manipulator (CDPM) is a special parallel manipulator in which the moving platform is driven by cables, instead of rigid links. In recent years, CDPMs have been researched extensively [1–6] because of their advantages to provide a light-weight structure, low moving mass, and large reachable workspace. A CDPM has a light-weight structure with low moving mass because the actuators are always mounted onto the base. Large workspace is achievable for a CDPM since the cables can be wound onto drums to provide very long length, unlike the rigid links with fixed lengths. These advantages make the CDPM a promising candidate for applications requiring high speed, high acceleration, and high payload but with moderate stiffness and accuracy [1–3]. Hence, CDPMs have been employed for service robots [4], rehabilitation systems [5], haptic devices [7] and long- range positioning devices [6]. CDPMs can be classified into two main categories, i.e. under-constrained CDPMs and fully-constrained CDPMs. Under- constrained CDPMs rely on additional constraints, such as gravity, to realize all the required Degrees of Freedom (DOF) but fully- constrained CDPMs can control all DOF with the cables only. For an n-DOF CDPM driven by m cables, it requires m ≥ n [8] if it is under-constrained and m ≥ n +1 [9] if it is fully-constrained. Due to cable unilateral driving property, where they can only pull but cannot push, tension analysis is the most essential issue for CDPM, as all the cables must always maintain positive tension. Therefore, the purpose of workspace analysis is to determine the moving platform poses that are kinematically feasible and in static equilibrium with positive cable tensions. Static workspace for under-constrained CDPMs contains poses that are able to counteract gravity with positive cable tensions. The NIST Robocrane [3] is an under-constrained CDPM which controls 6-DOF by six cables. Pusey [10] optimized a 6-DOF under- Mechanism and Machine Theory 46 (2011) 1265–1275 ⁎ Corresponding author. Tel.: + 65 67905568. E-mail addresses: limw0091@ntu.edu.sg (W.B. Lim), glyang@simtech.a-star.edu.sg (G. Yang), myeosh@ntu.edu.sg (S.H. Yeo), mustafa@simtech.a-star.edu.sg (S.K. Mustafa). 0094-114X/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2011.04.006 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt