Research Papers

A Buckling Flexure-Based Force-Limiting Mechanism

[+] Author and Article Information
Jonathan Slocum

77 Massachusetts Avenue, Room 3-253,
Cambridge, MA 02139
e-mail: jtslocum@mit.edu

Kenneth Kamrin

77 Massachusetts Avenue, Room 1-310,
Cambridge, MA 02139
e-mail: kkamrin@mit.edu

Alexander Slocum

77 Massachusetts Avenue, Room 3-461,
Cambridge, MA 02139
e-mail: slocum@mit.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received September 3, 2018; final manuscript received March 20, 2019; published online May 17, 2019. Assoc. Editor: Guimin Chen.

J. Mechanisms Robotics 11(4), 041004 (May 17, 2019) (8 pages) Paper No: JMR-18-1280; doi: 10.1115/1.4043317 History: Received September 03, 2018; Accepted March 21, 2019

A force-limiting buckling flexure has been created which can be used in a wide range of applications where excessive force from an implement can cause harm or damage. The buckling flexure is monolithic, contains no electronics, and can be manufactured using a single shot in an injection molding machine, making it cost effective. In this paper, the design of the flexure is applied to a force-limiting toothbrush as a design study to show its application in a real-world technology. An overview of the buckling flexure is presented, and a structural model is presented to predict when the flexure will elastically buckle. Flexures of different geometries were tested and buckled. The data show that the model can predict buckling of the flexure with an error of 20.84%. A finite element model was also performed which predicts buckling of the flexure within an error of 25.35%. Furthermore, a preliminary model is presented which enables the design of the buckling beam’s displacement, such that the total breakaway deformation can be maximized, making sensing the sudden deformation easier to detect. As part of the application of the buckling flexure, an ergonomic, injection moldable toothbrush was created with the flexure built into the neck of the brush. When the user applies too much force while brushing, the flexure gives way and alerts the user when they have applied too much force; when the user lets off the force, the brush snaps back to its original shape. This design methodology is generalized and can be utilized in other force limited applications where an injection-moldable, pre-set force, and purely mechanical breakaway device is desired.

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Krüger, J., Lien, T. K., and Verl, A., 2009, “Cooperation of Human and Machines in Assembly Lines,” CIRP Ann.—Manuf. Technol., 58(2), pp. 628–646. [CrossRef]
De Santis, A., Siciliano, B., De Luca, A., and Bicchi, A., 2008, “An Atlas of Physical Human-Robot Interaction,” Mech. Mach. Theory, 43(3), pp. 253–270. [CrossRef]
Zhang, M., Laliberté, T., and Gosselin, C., 2017, “Design and Static Analysis of Elastic Force and Torque Limiting Devices for Safe Physical Human–Robot Interaction,” J. Mech. Robot., 9(2), p. 021003. [CrossRef]
Canadian Dental Hygienists Association, 2006, “CDHA Position Paper on Tooth Brushing/Déclaration de L’ACHD Sur Le Brossage Des Dents,” Can. J. Dent. Hyg., 40(5), pp. 1–14. https://www.cdha.ca/pdfs/Profession/Resources/tooth_brushing_paper_reprint.pdf
White, L., and Ingels, L., 1984, “Pressure Sensing Device for Holding a Toothbrush,” U.S. Patent No. 4,476,604.
Dirksing, R., 1992, “Toothbrush Having Handle Joined to Brush Head by Non-Pinching Flexible Twin Beam Structure,” U.S. Patent No. 5,105,499.
Piserchio, R., 2011, “Pressure-Sensitive Toothbrush,” U.S. Patent No. 20110016651A1.
Irizarry, J., 1994, “Pressure Alarm Toothbrush Assembly,” U.S. Patent No. 5,331,707.
Craig, J. J., 1981, “Hybrid Position/Force Control of Manipulators,” J. Dyn. Syst. Meas. Control, 103(2), pp. 126–133. [CrossRef]
Daniel, E. W., 1977, “Force Feedback Control of Manipulator Fine Motions,” J. Dyn. Syst. Meas. Control, 99(2), pp. 91–97. [CrossRef]
Rosenberg, L. B., and Jackson, B. G., 2002, “Force Feedback Device Including Flexure Member Between Actuator and User Object,” U.S. Patent No. 6,437,771.
Das, H., Ohm, T. R., and Steele, R. D., 2002, “Tool Actuation and Force Feedback On Robot-Assisted Microsurgery System,” U.S. Patent No. 6,385,509.
Pierrot, F., Dombre, E., Dégoulange, E., Urbain, L., Caron, P., Boudet, S., Gariépy, J., and Mégnien, J. L., 1999, “Hippocrate: A Safe Robot Arm for Medical Applications With Force Feedback,” Med. Image Anal., 3(3), pp. 285–300. [CrossRef] [PubMed]
Kramer, H., 2001, “Toothbrush Comprising a Flexibly Linked Region in the Head,” U.S. Patent No. 6,185,779.
Jungnickel, U., Altmann, N., and Guebler, R., 2014, “Force Sensing Oral Care Instrument,” U.S. Patent No. 8,832,895.
Fox, R., Hippen, J., Knaub, D., Resuello, I., Frank, P., and Moskovich, R., 2003, “Replaceable Head Toothbrush Providing Controlled Brushing Pressure,” U.S. Patent No. 6,502,272.
Giuliani, D., McMahon, R. W., and McInnes, C., 1998, “Toothbrush With Adaptive Load Sensor,” U.S. Patent No. 5,784,742.
Huefner, N. F., and Burrell, F. J., 1994, “Toothbrush Having Adjustable Brushing Pressure,” U.S. Patent No. 5,315,732.
Heinzelman, B. D., Lamond, D. R., and Fontayne, D., 1998, “Resiliently Flexible Toothbrush,” U.S. Patent No. 5,735,012.
Sundius, C. L., and Mcfadden, B. P., 1999, “Pressure Sensing Toothbrush,” U.S. Patent No. 5,876,207.
Mierau, H.-D., and Spindler, T., 1987, “Toothbrush,” U.S. Patent No. 4,698,869.
Gao, Z., and Zhang, D., 2012, “Flexure Parallel Mechanism: Configuration and Performance Improvement of a Compact Acceleration Sensor,” J. Mech. Robot., 4(3), p. 031002. [CrossRef]
Wei, Y., and Xu, Q., 2016, “Design of a Force Sensor Based on Flexure Beams With Piezoresistive and PVDF Elements,” Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Charlotte, NC, Aug. 21–24, pp. 1–7.
Zhang, X., Wang, G., and Xu, Q., 2018, “Design, Analysis and Testing of a New Compliant Compound Constant-Force Mechanism,” Actuators, 7(4), p. 65. [CrossRef]
Brenner, M. P., Lang, J. H., Li, J., Qiu, J., and Slocum, A. H., 2003, “Optimal Design of a Bistable Switch,” Proc. Natl. Acad. Sci. U.S.A., 100(17), pp. 9663–9667. [CrossRef] [PubMed]
Li, J., Brenner, M. P., Christen, T., Kotilainen, M. S., Lang, J. H., and Slocum, A. H., 2005, “Deep-Reactive Ion-Etched Compliant Starting Zone Electrostatic Zipping Actuators,” J. Microelectromech. Syst., 14(6), pp. 1283–1297. [CrossRef]
An, S., Kim, B., Kwon, S., Moon, G., Lee, M., and Jhe, W., 2018, “Bifurcation-Enhanced Ultrahigh Sensitivity of a Buckled Cantilever,” Proc. Natl. Acad. Sci. U.S.A., 115(12), pp. 2884–2889. [CrossRef] [PubMed]
Dobrokhotov, V. V., Yazdanpanah, M. M., Pabba, S., Safir, A., and Cohn, R. W., 2008, “Visual Force Sensing With Flexible Nanowire Buckling Springs,” Nanotechnology, 19(3), p. 035502. [CrossRef] [PubMed]
She, Y., Li, C., Cleary, J., and Su, H.-J., 2015, “Design and Fabrication of a Soft Robotic Hand With Embedded Actuators and Sensors,” J. Mech. Robot., 7(2), p. 021007. [CrossRef]
Rosema, N. A. M., Adam, R., Grender, J. M., Van der Sluijs, E., Supranoto, S. C., and Van der Weijden, G. A., 2014, “Gingival Abrasion and Recession in Manual and Oscillating-Rotating Power Brush Users,” Int. J. Dent. Hyg., 12(4), pp. 257–266. [CrossRef] [PubMed]
Löe, H., 2000, “Oral Hygiene in the Prevention of Caries and Periodontal Disease,” Int. Dent. J., 50(3), pp. 129–139. [CrossRef] [PubMed]
Timoshenko, S., 1936, Theory of Elastic Stability, McGraw-Hill Book Company Inc., New York.


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Fig. 1

(a) Toothbrush with buckling beam and stiffening anvil to alert users when they are exerting too much force while brushing. (b) A close-up of the buckling flexure where the buckled beam is pressing against the stiffening anvil. The anvil serves three purposes: to provide an audible click when the buckling beam strikes, to limit travel (and stress) of the buckled beam, and couple the two beams together to stiffen the structure post-buckling to ensure the device will not plastically deform or break. This protects both the user and the device from harm.

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Fig. 2

(a) The simplified structure imprinted on the original brush and (b) the structure with labeled dimensions and angles used in the following analysis as well as a free-body diagram of the structure with resultant forces. Note that Fin has been broken into its xy vector components F1 and F2.

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Fig. 3

Large deflection of a slender buckled column with clamped and free end boundary conditions, respectively. This represents one-fourth of the total length of the buckling beam shape.

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Fig. 4

Deformed shape of the buckling beam—note that it is the shape of a cosine function

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Fig. 5

A test buckling flexure cut from polycarbonate. Mounting holes allow the flexure to be clamped securely for force displacement testing. A notch was created at a known distance from the flexure to ensure samples were repeatedly tested in the same position.

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Fig. 6

Test setup to deform the polycarbonate testing flexures. Three main components allow the force–displacement of the buckling flexure to be measured: the testing flexure itself, a fixed testing mount, and an actuated load cell.

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Fig. 7

Solid model of one of the test flexures showing the constraints and loads used for the finite element analysis and the mesh used for the buckling simulation. The test flexures were clamped at the bolt holes and the force was applied at the same notch that was used for the real measurements of the test flexures.

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Fig. 8

Force–displacement data for test flexures with different buckling beam thicknesses. Only one set of flexures with each thickness was measured. As beam thickness increases, the critical buckling load (first peak in the plots) of the structure also increases. Once the buckling beam conforms to the anvil, the structure stiffens again, as shown by the change of slope after approximately 3 mm of displacement.

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Fig. 9

Sample buckling flexure designed to mate with a removable handle and toothbrush head. This flexure can be used for brushing and can be compactly stored.



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