Strain Gauges Based 3D Shape Monitoring of Beam Structures Using Finite Width Gauge Model
This paper presents a new approach validated experimentally to reconstruct with strain gauges the deformed shape of a straight beam with circular cross section. It is based on a novel beam-specific strain gauge model that improves the strain measurement by taking into account the width of the gauges. These improved strain measurements are used by a 3D finite strain large displacement beam shape reconstruction method to recover the deformed shape iteratively. The whole reconstruction approach has been validated experimentally with 3D deformations of a beam instrumented with strain gauges. Results show that the strain gauge model developed improves reconstruction accuracy and that beam reconstruction can be achieved effectively.
KeywordsBeam monitoring 3D reconstruction Shape reconstruction Strain sensor Strain measurement
This work is part of the project GAME-D, financed by the French National Agency for Research (ref: ANR-12-TECS-0019) and supported by Laboratory of Excellence CAMI (ref: ANR-11-LABX-0004-01).
The authors would like to thank Cecilia Hughes for English corrections and P. A. Barraud for providing valuable advice concerning electronic instrumentation.
Compliance with Ethical Standards
Conflict of interests
On behalf of all authors, the corresponding author states that there is no conflict of interest.
- 8.Cali M, Oliveri SM, Ambu R, Fichera G (2018) An integrated approach to characterize the dynamic behaviour of a mechanical chain tensioner by functional tolerancing. Stroj Vestn-J Mech E 64(4):245–257Google Scholar
- 12.Todd MD, Stull CJ, Dickerson M (2013) A local material basis solution approach to reconstructing the three-dimensional displacement of rod-like structures from strain measurements. Journal of Applied Mechanics 80(4)Google Scholar
- 14.Chadha M, Todd MD (2017) A generalized approach for reconstructing the three-dimensional shape of slender structures including the effects of curvature, shear, torsion, and elongation. J Appl Mech 84(4):041003Google Scholar
- 15.Henken KR, Dankelman J, van den Dobbelsteen JJ, Cheng LK, van der Heiden MS (2014) Error analysis of fbg-based shape sensors for medical needle tracking. 19,(5),1523–1531. https://doi.org/10.1109/TMECH.2013.2287764
- 16.Sigurdardottir DH, Stearns J, Glisic B (2017) Error in the determination of the deformed shape of prismatic beams using the double integration of curvature. Smart Materials and Structures 26(7). http://stacks.iop.org/0964-1726/26/i=7/a=075002
- 21.Childlers B, Gifford D, Duncan R, Raum M, Vercellino M (2006) Fiber optic position and shape sensing device and method relating thereto. US Patent App 11(/180):389Google Scholar
- 23.Xu H, Ren WX, Wang ZC (2015) Deflection estimation of bending beam structures using fiber bragg grating strain sensors. Adv Struct Eng 18(3):395–403Google Scholar
- 24.Reissner E (1973) On one-dimensional large-displacement finite-strain beam theory. Stud Appl Math 52 (2):87–95Google Scholar
- 25.Ryu SC, Dupont PE (2014) Fbg-based shape sensing tubes for continuum robots. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp 3531–3537. https://doi.org/10.1109/ICRA.2014.6907368
- 26.Hoffmann K (1989) An introduction to measurements using strain gages. Hottinger Baldwin Messtechnik DarmstadtGoogle Scholar
- 27.Abayazid M, Kemp M, Misra S (2013) 3d flexible needle steering in soft-tissue phantoms using fiber bragg grating sensors. In: Proc. IEEE international conference on robotics and automation (ICRA), pp 5843–5849. https://doi.org/10.1109/ICRA.2013.6631418
- 28.Schajer GS (1993) Use of displacement data to calculate strain gauge response in non-uniform strain fields. Strain 29(1):9–13. https://doi.org/10.1111/j.1475-1305.1993.tb00820.x Google Scholar
- 29.Schaefer PL, Chagnon G, Moreau-Gaudry A (2016) Advanced sensors placement for accurate 3d needle shape reconstruction. In: 2016 IEEE 38th annual international conference of the engineering in medicine and biology society (EMBC). IEEE, pp 5132–5135Google Scholar
- 30.Wang W, Jüttler B, Zheng D, Liu Y (2008) Computation of rotation minimizing frames. ACM Trans Graph (TOG) 27(1):2Google Scholar
- 31.Hairer E, Wanner G, Lubich C (2006) Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ednGoogle Scholar
- 34.Kim B, Ha J, Park FC, Dupont PE (2014) Optimizing curvature sensor placement for fast, accurate shape sensing of continuum robots. In: 2014 IEEE international conference on robotics and automation (ICRA), pp 5374–5379. https://doi.org/10.1109/ICRA.2014.6907649
- 35.Mahoney AW, Bruns TL, Swaney PJ, Webster RJ (2016) On the inseparable nature of sensor selection, sensor placement, and state estimation for continuum robots or where to put your sensors and how to use them. In: 2016 IEEE international conference on robotics and automation (ICRA). IEEE, pp 4472–4478Google Scholar
- 38.Hammond FL, Smith MJ, Wood RJ (2014) Estimating surgical needle deflection with printed strain gauges. In: 2014 36th annual international conference of the IEEE engineering in medicine and biology society, pp 6931–6936. https://doi.org/10.1109/EMBC.2014.6945222