Articles | Volume 7, issue 1
https://doi.org/10.5194/ms-7-107-2016
https://doi.org/10.5194/ms-7-107-2016
Research article
 | 
08 Apr 2016
Research article |  | 08 Apr 2016

Solving the double-banana rigidity problem: a loop-based approach

Florian Simroth, Huafeng Ding, and Andrés Kecskeméthy

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Cited articles

Abel, U. and Bicker, R.: Determination of All Minimal Cut-Sets between a Vertex Pair in an Undirected Graph, IEEE T. Reliab., R-31, 167–171, 1982.
Agrawal, V. and Rao, J.: Fractionated Freedom Kinematic Chains and Mechanisms, Mech. Mach. Theory, 22, 125–130, 1987.
Bennett, D. J. and Hollerbach, J. M.: Autonomous calibration of single-loop closed kinematic chains formed by manipulators with passive endpoint constraints, IEEE T. Robotic. Autom. 7, 597–606, 1991.
Carretero, J., Podhorodeski, R., Nahon, M., and Gosselin, C. M.: Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator, J. Mech. Design, 122, 17–24, 2000.
Casals, A. and Amat, J.: Automatic Guidance of an Assistant Robot in Laparoscopic Surgery, in: Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, April 1996, 895–900, 1996.
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Short summary
The "double-banana" problem is a counter-example of Laman's rigidity condition formula for which existing standard Degree of Freedom counting formulas fail. The novelty of the approach for rigidity detection presented in this paper consists in regarding the structure not as a set of joint-connected bodies but as a set of interconnected loops. By tracking isolated DOFs such as those arising between pairs of spherical joints, rigidity/mobility subspaces can be identified successfully.