“On the Mobility and Fault Tolerance of Closed Chain Manipulators with Passive Joints”

Authors: Pål J. From and Jan T. Gravdahl,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 2008, Vol 29, No 4, pp. 151-165.

Keywords: Robotics, kinematics, mobility, fault tolerance

Abstract: A systematic analysis of the mobility of closed chain manipulators with passive joints is presented. The main observation in this paper is that the mobility of the manipulator, considering the passive joints only, should always be zero. Further, for the manipulator to be fault tolerant, the mobility should remain zero when actuator failure occurs for an arbitrary joint. We present a simple and rigorous approach to the problem of finding the smallest set of active joints for which the manipulator remains equilibrated with respect to free swinging joint failure in any joint. Several examples of how to choose the active joints for different mechanisms to guarantee that the manipulator is equilibrated and fault tolerant are presented.

PDF PDF (698 Kb)        DOI: 10.4173/mic.2008.4.3

DOI forward links to this article:
[1] Hamid Abdi, Saeid Nahavandi, Yakov Frayman and Anthony A. Maciejewski (2012), doi:10.1017/S0263574711000671
[2] Cong Dung Pham, Pål Johan From and Jan Tommy Gravdahl (2014), doi:10.4236/am.2014.516247
[3] Cong Dung Pham and Pal Johan From (2014), doi:10.1109/ROBIO.2014.7090632
[4] Cong Dung Pham and Pal Johan From (2015), doi:10.1109/ROBIO.2015.7418969
[5] Pål Johan From, Anders Robertsson and Rolf Johansson (2014), doi:10.3182/20140824-6-ZA-1003.02498
[6] Lars Grimstad, Marco F.S. Xaud, Antonio C. Leite and Pål J. From (2017), doi:10.1016/j.ifacol.2017.08.1811
[7] Mehul M Gor, PM Pathak, AK Samantaray, Jung Ming Yang and SW Kwak (2017), doi:10.1177/0959651817743410
[8] Pål Johan From and Jan Tommy Gravdahl (2009), doi:10.3182/20090630-4-ES-2003.00203
[9] Pål Johan From, Cong Dung Pham and Jan Tommy Gravdahl (2014), doi:10.1002/pamm.201410027
[10] Adrian Peidro, Pedro David Perez-Navarro, Rafael Puerto, Luis Paya and Oscar Reinoso (2023), doi:10.1016/j.mechmachtheory.2023.105403
[1] DAI, J.S., H., Z., LIPKIN, H. (2006). Mobility of over-constrained parallel mechanisms, Transactions of ASME, 128.
[2] FROM, P.J. GRAVDAHL, J.T. (2009). Fault tolerance of parallel manipulators with passive joints, Submitted to SafeProcess, Barcelona, Spain.
[3] HERVÉ, J.M. (1978). Analyse structurelle des mécanismes par groupe des déplacements, Mechanism Machine Theory, 1.4.
[4] LIPKIN, H. DUFFY, J. (2002). Sir Robert Stawell Ball and methodologies of modern screw theory, Proc. of Journal of Mechanical Engineering Science, 216 No 1.
[5] MATONE, R. ROTH, B. (1999). In-parallel manipulators: A framework on how to model actuation schemes and a study of their effects on singular postures, Trans. of ASME, 121.
[6] MENG, J., LIU, G., LI, Z. (2007). A geometric theory for analysis and synthesis of sub-6 dof parallel manipulators, IEEE Transactions on Robotics, 23, no. 4 doi:10.1109/TRO.2007.898995
[7] MURRAY, R.M., LI, Z., SASTRY, S. (1994). A mathematical introduction to robotic manipulation, CRC Press.
[8] RICO, J., GALLARDO, J., RAVANI, B. (2003). Lie algebra and the mobility of kinematic chains, Journal of Robotic Systems, 20, no. 8 doi:10.1002/rob.10099
[9] RICO, J.M., AGUILERA, L.D., GALLARDO, J., RODRIGUEZ, R., OROZCO, H., BARRERA, J.M. (2006). A more general mobility criterion for parallel mechanisms, Journal of Mechanical Design, 128.
[10] TINÓS, R., TERRA, M.H., BERGERMAN, M. (2006). A fault tolerance framework for cooperative robotic manipulator, Control Engineering Practice. 15:615-625 doi:10.1016/j.conengprac.2006.10.018

  title={{On the Mobility and Fault Tolerance of Closed Chain Manipulators with Passive Joints}},
  author={From, Pål J. and Gravdahl, Jan T.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}