A Geometric Approach to the Design of Serial and Parallel Manipulators with Passive Joints


The use of robotic manipulators in remote and sensitive areas calls for more robust solutions when handling joint failure, and the industry demands mathematically robust approaches to handle even the worst case scenarios. For both serial and parallel manipulators torque failure is indeed a worst case scenario. Thus, a systematic analysis of the effects of external forces on manipulators with passive joints is presented. For serial manipulators we find under what conditions the robot is conditionally equilibrated, that is, equilibrated with respect to a specific external force. These conditions are, as expected, very restrictive. The serial, or subchain, case serves as a good platform for analyzing parallel manipulators. In parallel manipulators passive joints can appear as a design choice or as a result of torque failure. In both cases a good understanding of the effects that passive joints have on the mobility and motion of the parallel manipulator is crucial. We first look at the effects that passive joints have on the mobility of the mechanism. Then, if the mobility considering passive joints only is not zero we find a condition similar to the serial case for which the parallel manipulator is conditionally equilibrated with respect to a specific external force.

Share and Cite:

Pham, C. , From, P. and Gravdahl, J. (2014) A Geometric Approach to the Design of Serial and Parallel Manipulators with Passive Joints. Applied Mathematics, 5, 2585-2601. doi: 10.4236/am.2014.516247.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Matone, R. and Roth, B. (1999) In-Parallel Manipulators: A Framework on How to Model Actuation Schemes and a Study of Their Effects on Singular Postures. Transaction of ASME, 121, 2-8.
[2] Liu, Y.H., Xu, Y. and Bergerman, M. (1999) Cooperation Control of Multiple Manipulators with Passive Joints. IEEE Transactions on Robotics and Automation, 15, 258-267.
[3] Bicchi, A. and Prattichizzo, D. (2000) Manipulability of Cooperating Robots with Unactuated Joints and Closed-Chain Mechanisms. IEEE Transaction of Robotics and Automation, 16, 336-345.
[4] Murray, R.M., Li, Z. and Sastry, S.S. (1994) A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton.
[5] Dai, J.S., Huang, Z. and Lipkin, H. (2006) Mobility of Overconstrained Parallel Mechanisms. Transactions of ASME, 128, 220-229.
[6] Rico, J.M., Gallardo, J. and Ravani, B. (2003) Lie Algebra and the Mobility of Kinematic Chains. Journal of Robotic Systems, 20, 477-499.
[7] Rico, J.M., Aguilera, L.D., Gallardo, J., Rodriguez, R., Orozco, H. and Barrera, J.M. (2006) A More General Mobility Criterion for Parallel Mechanisms. Journal of Mechanical Design, 128, 207-219.
[8] English, J.D. and Maciejewski, A.A. (1998) Fault Tolerance for Kinematically Redundant Manipulators: Anticipating Free-Swinging Joint Failures. IEEE Transactions of Robotics and Automation, 14, 566-575.
[9] Tinos, R. and Terra, M.H. (2002) Control of Cooperative Manipulators with Passive Joints. American Control Conference, Anchorage, 1129-1134.
[10] Tinós, R., Terra, M.H. and Bergerman, M. (2007) A Fault Tolerance Framework for Cooperative Robotic Manipulators. Control Engineering Practice, 15, 615-625.
[11] Oriolo, G. and Nakamura, Y. (1991) Free-Joint Manipulators: Motion Control under Second-Order Nonholonomic Constraints. Proceedings of IEEE International Workshop on Intelligent Robots and Systems, Osaka, 3-5 November 1991, 1248-1253.
[12] Arai, H. and Tachi, S. (1990) Dynamic Control of a Manipulator with Passive Joints-Position Control Experiments by a Prototype Manipulator. IEEE/RSJ International Conference on Intelligent Robots and Systems, Ibaraki, 3-6 July 1990, 935-940.
[13] Hauser, J. and Murray, R.M. (1990) Nonlinear Controllers for Non-Integrable Systems: The Acrobat Example. American Control Conference, San Diego, 23-25 May 1990, 669-671.
[14] From, P.J. and Gravdahl, J.T. (2008) On the Mobility and Fault Tolerance of Closed Chain Manipulators with Passive Joints. Modeling, Identification and Control, 29, 151-165.
[15] Meng, J., Liu, G. and Li, Z. (2007) A Geometric Theory for Analysis and Synthesis of Sub-6 DoF Parallel Manipulators. IEEE Transactions on Robotics, 23, 625-649.
[16] From, P.J., Pettersen, K.Y. and Gravdahl, J.T. (2014) Vehicle-Manipulator Systems: Modeling for Simulation, Analysis, and Control. Springer Verlag, London.
[17] From, P.J., Gravdahl, J.T. and Abbeel, P. (2010) On the Influence of Ship Motion Prediction Accuracy on Motion Planning and Control of Robotic Manipulators on Seaborne Platforms. Proceedings of International Conference of Robotics and Automation, Anchorage, 3-7 May 2010, 5281-5288.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.