Experimental Techniques

, Volume 43, Issue 5, pp 599–611 | Cite as

Strain Gauges Based 3D Shape Monitoring of Beam Structures Using Finite Width Gauge Model

  • P.-L. SchaeferEmail author
  • G. Barrier
  • G. Chagnon
  • T. Alonso
  • A. Moreau-Gaudry


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.


Beam 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.


  1. 1.
    Abdel-Jaber H, Glisic B (2015) Analysis of the status of pre-release cracks in prestressed concrete structures using long-gauge sensors. Smart Mater Struct 24(2):25–38. Google Scholar
  2. 2.
    Lee JJ, Shinozuka M (2006) Real-time displacement measurement of a flexible bridge using digital image processing techniques. Exp Mech 46(1):105–114. Google Scholar
  3. 3.
    Xia Y, Zhang P, qing Ni Y, ping Zhu H (2014) Deformation monitoring of a super-tall structure using real-time strain data. Eng Struct 67(Supplement C):29–38. Google Scholar
  4. 4.
    Park YL, Elayaperumal S, Daniel B, Ryu SC, Shin M, Savall J, Black R, Moslehi B, Cutkosky M (2010) Real-time estimation of 3-d needle shape and deflection for mri-guided interventions. IEEE/ASME Trans Mechatron 15(6):906–915. Google Scholar
  5. 5.
    Roesthuis R, Kemp M, van den Dobbelsteen J, Misra S (2014) Three-dimensional needle shape reconstruction using an array of fiber bragg grating sensors. IEEE/ASME Trans Mechatron 19(4):1115–1126. Google Scholar
  6. 6.
    Lehmann T, Rossa C, Usmani N, Sloboda RS, Tavakoli M (2016) A real-time estimator for needle deflection during insertion into soft tissue based on adaptive modeling of needle. IEEE/ASME Trans Mechatron 21 (6):2601–2612. Google Scholar
  7. 7.
    Logozzo S, Kilpela A, Makynen A, Zanetti EM, Franceschini G (2014) Recent advances in dental optics part ii: Experimental tests for a new intraoral scanner. Opt Lasers Eng 54:187–196. Google Scholar
  8. 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
  9. 9.
    Yan X, Huang W, Kwon SR, Yang S, Jiang X, Yuan FG (2013) A sensor for the direct measurement of curvature based on flexoelectricity. Smart Mater Struct 22(8):085016. Google Scholar
  10. 10.
    Glaser R, Caccese V, Shahinpoor M (2012) Shape monitoring of a beam structure from measured strain or curvature. Exp Mech 52(6):591–606. Google Scholar
  11. 11.
    Cheng B, Zhu W, Liu J, Yuan L, Xiao H (2017) 3d beam shape estimation based on distributed coaxial cable interferometric sensor. Smart Mater Struct 26(3):35–44. Google Scholar
  12. 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
  13. 13.
    Gherlone M, Cerracchio P, Mattone M, Sciuva MD, Tessler A (2014) An inverse finite element method for beam shape sensing: theoretical framework and experimental validation. Smart Mater Struct 23(4):45–57. Google Scholar
  14. 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. 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.
  16. 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).
  17. 17.
    Wang ZC, Geng D, Ren WX, Liu HT (2014) Strain modes based dynamic displacement estimation of beam structures with strain sensors. Smart Mater Struct 23(12):125–133. Google Scholar
  18. 18.
    Kim NS, Cho NS (2004) Estimating deflection of a simple beam model using fiber optic bragg-grating sensors. Exp Mech 44(4):433–439. Google Scholar
  19. 19.
    Moon H, Jeong J, Kang S, Kim K, Song YW, Kim J (2014) Fiber-bragg-grating-based ultrathin shape sensors displaying single-channel sweeping for minimally invasive surgery. Opt Lasers Eng 59:50–55. Google Scholar
  20. 20.
    Wang H, Zhang R, Chen W, Liang X, Pfeifer R (2016) Shape detection algorithm for soft manipulator based on fiber bragg gratings. IEEE/ASME Trans Mechatron 21(6):2977–2982. Google Scholar
  21. 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
  22. 22.
    Xu R, Yurkewich A, Patel RV (2016) Curvature, torsion, and force sensing in continuum robots using helically wrapped fbg sensors. IEEE Robot Autom Lett 1(2):1052–1059. Google Scholar
  23. 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. 24.
    Reissner E (1973) On one-dimensional large-displacement finite-strain beam theory. Stud Appl Math 52 (2):87–95Google Scholar
  25. 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.
  26. 26.
    Hoffmann K (1989) An introduction to measurements using strain gages. Hottinger Baldwin Messtechnik DarmstadtGoogle Scholar
  27. 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.
  28. 28.
    Schajer GS (1993) Use of displacement data to calculate strain gauge response in non-uniform strain fields. Strain 29(1):9–13. Google Scholar
  29. 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. 30.
    Wang W, Jüttler B, Zheng D, Liu Y (2008) Computation of rotation minimizing frames. ACM Trans Graph (TOG) 27(1):2Google Scholar
  31. 31.
    Hairer E, Wanner G, Lubich C (2006) Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ednGoogle Scholar
  32. 32.
    Magnus W (1954) On the exponential solution of differential equations for a linear operator. Commun Pur Appl Math 7(4):649–673. Google Scholar
  33. 33.
    Simo J, Fox D (1989) On a stress resultant geometrically exact shell model. part i: Formulation and optimal parametrization. Comput Methods Appl Mech Eng 72(3):267–304. Google Scholar
  34. 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.
  35. 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
  36. 36.
    Gu M, Piedbuf JC (2003) A flexible-arm as manipulator position and force detection unit. Control Eng Pract 11(12):1433 – 1448., award winning applications-2002 IFAC World CongressGoogle Scholar
  37. 37.
    Payo I, Feliu V (2014) Strain gauges based sensor system for measuring 3-d deflections of flexible beams. Sens Actuators A: Phys 217(Supplement C):81–94. Google Scholar
  38. 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.
  39. 39.
    Bonvilain A, Gangneron M (2016) Characterization of strain microgauges for the monitoring of the deformations of a medical needle during its insertion in human tissues. Microsyst Technol 22(3):551–556. Google Scholar

Copyright information

© The Society for Experimental Mechanics, Inc 2019

Authors and Affiliations

  1. 1.TIMC-IMAG, Université Grenoble Alpes, CNRS, CHU Grenoble Alpes, Institute of Engineering Université Grenoble AlpesGrenobleFrance

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