Research Papers: Mechanisms and Robotics

MEMS-Based Conjugate Surfaces Flexure Hinge

[+] Author and Article Information
Matteo Verotti

Department of Mechanical and
Aerospace Engineering,
Sapienza University of Rome,
Rome 00184, Italy
e-mail: matteo.verotti@uniroma1.it

Rocco Crescenzi

Department of Information Engineering,
Electronic and Telecommunications,
Sapienza University of Rome,
Rome 00184, Italy
e-mail: crescenzi@die.uniroma1.it

Marco Balucani

Department of Information Engineering,
Electronic and Telecommunications,
Sapienza University of Rome,
Rome 00184, Italy
e-mail: balucani@die.uniroma1.it

Nicola P. Belfiore

Department of Mechanical and
Aerospace Engineering,
Sapienza University of Rome,
Rome 00184, Italy
e-mail: belfiore@dima.uniroma1.it

See http://www.ansys.com/ for more information.

See http://www.nanotechnik.com/ for more information.

See http://www.xcitex.com/ for more information.

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 16, 2014; final manuscript received October 5, 2014; published online November 14, 2014. Assoc. Editor: Shorya Awtar.

J. Mech. Des 137(1), 012301 (Jan 01, 2015) (10 pages) Paper No: MD-14-1242; doi: 10.1115/1.4028791 History: Received April 16, 2014; Revised October 05, 2014; Online November 14, 2014

This paper presents a new concept flexure hinge for MEMS applications and reveals how to design, construct, and experimentally test. This hinge combines a curved beam, as a flexible element, and a pair of conjugate surfaces, whose contact depends on load conditions. The geometry is conceived in such a way that minimum stress conditions are maintained within the flexible beam. A comparison of the new design with the other kind of revolute and flexible joints is presented. Then, the static behavior of the hinge is analyzed by means of a theoretical approach, based on continuum mechanics, and the results are compared to those obtained by means of finite element analysis (FEA) simulation. A silicon hinge prototype is also presented and the construction process, based on single step lithography and reactive ion etching (RIE) technology, is discussed. Finally, a crucial in–SEM experiment is performed and the experimental results are interpreted through the theoretical models.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Wang, D., Yang, Q., and Dong, H., 2013, “A Monolithic Compliant Piezoelectric-Driven Microgripper: Design, Modeling, and Testing,” IEEE/ASME Trans. Mech., 18(1), pp. 138–147. [CrossRef]
Belfiore, N. P., Verotti, M., Crescenzi, R., and Balucani, M., 2013, “Design, Optimization and Construction of MEMS Based Micro Grippers for Cell Manipulation,” IEEE International Conference on System Science and Engineering, ICSSE 2013, IEEE, Budapest, Hungary, July 4–6, pp. 105–110. [CrossRef]
Yi, B.-J., Chung, G. B., Na, H. Y., Kim, W. K., and Suh, I. H., 2003, “Design and Experiment of a 3-DOF Parallel Micromechanism Utilizing Flexure Hinges,” IEEE Trans. Rob. Autom., 19(4), pp. 604–612. [CrossRef]
Tian, Y., and Shirinzadeh, B., 2009, “Development of a Flexure-Based 3-RRR Parallel Mechanism for Nano-Manipulation,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Singapore, July 14–17, AIM 2009, IEEE, July 4–6, pp. 1324–1329. [CrossRef]
Belfiore, N. P., EmamiMeibodi, M., Verotti, M., Crescenzi, R., Balucani, M., and Nenzi, P., 2013, “Kinetostatic Optimization of a MEMS Based Compliant 3 DOF Plane Parallel Platform,” IEEE 9th International Conference on Computational Cybernetics, ICCC 2013, IEEE, Tihany, Hungary, July 8–10, pp. 261–266. [CrossRef]
Bashash, S., and Jalili, N., 2009, “Robust Adaptive Control of Coupled Parallel Piezo-Flexural Nanopositioning Stages,” IEEE/ASME Trans. Mech., 14(1), pp. 11–20. [CrossRef]
Polit, S., and Dong, J., 2011, “Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-Nanomanufacturing,” IEEE/ASME Trans. Mech., 16(4), pp. 724–733. [CrossRef]
Xu, Q., 2012, “Design and Development of a Flexure-Based Dual-Stage Nanopositioning System With Minimum Interference Behavior,” IEEE Trans. Autom. Sci. Eng., 9(3), pp. 554–563. [CrossRef]
Howell, L., 2001, Compliant Mechanisms, Wiley-Interscience, New York.
Lobontiu, N., 2010, Compliant Mechanisms: Design of Flexure Hinges, CRC, Boca Raton, FL.
Pei, X., Yu, J., Zong, G., Bi, S., and Su, H., 2009, “The Modeling of Cartwheel Flexural Hinges,” Mech. Mach. Theory, 44(10), pp. 1900–1909. [CrossRef]
Cannon, J., and Howell, L., 2005, “A Compliant Contact-Aided Revolute Joint,” Mech. Mach. Theory, 40(11), pp. 1273–1293. [CrossRef]
Bellouard, Y., 2010, Microrobotics: Methods and Applications, CRC, Boca Raton, FL.
Bazaz, S. A., Khan, F., and Shakoor, R. I., 2011, “Design, Simulation and Testing of Electrostatic SOI Mumps Based Microgripper Integrated With Capacitive Contact Sensor,” Sens. Actuators, A, 167(1), pp. 44–53. [CrossRef]
Beyeler, F., Neild, A., Oberti, S., Bell, D., Sun, Y., Dual, J., and Nelson, B., 2007, “Monolithically Fabricated Microgripper With Integrated Force Sensor for Manipulating Microobjects and Biological Cells Aligned in an Ultrasonic Field,” J. Microelectromech. Syst., 16(1), pp. 7–15. [CrossRef]
Chen, G.-M., Jia, J.-Y., and Li, Z.-W., 2005, “On Hybrid Flexure Hinges,” Proceedings on Networking, Sensing and Control, IEEE, Tucson, AZ, Mar. 19–22, pp. 700–704. [CrossRef]
Lee, V., Gibert, J., and Ziegert, J., 2013, “Hybrid Bi-Directional Flexure Joint,” Precis. Eng., 38(2), pp. 270–278. [CrossRef]
Yong, Y. K., Lu, T.-F., and Handley, D. C., 2008, “Review of Circular Flexure Hinge Design Equations and Derivation of Empirical Formulations,” Precis. Eng., 32(2), pp. 63–70. [CrossRef]
Lobontiu, N., Garcia, E., Goldfarb, M., and Paine, J. S., 2001, “Corner-Filleted Flexure Hinges,” ASME J. Mech. Des., 123(3), pp. 346–352. [CrossRef]
Lobontiu, N., Paine, J. S., O'Malley, E., and Samuelson, M., 2002, “Parabolic and Hyperbolic Flexure Hinges: Flexibility, Motion Precision and Stress Characterization Based on Compliance Closed-Form Equations,” Precis. Eng., 26(2), pp. 183–192. [CrossRef]
Smith, S. T., Badami, V. G., Dale, J. S., and Xu, Y., 1997, “Elliptical Flexure Hinges,” Rev. Sci. Instrum., 68(3), pp. 1474–1483. [CrossRef]
Xu, P., Jingjun, Y., Guanghua, Z., and Shusheng, B., 2008, “The Stiffness Model of Leaf-Type Isosceles-Trapezoidal Flexural Pivots,” ASME J. Mech. Des., 130(8), p. 082303. [CrossRef]
Zhang, S., and Fasse, E., 2001, “A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge,” ASME J. Mech. Des., 123(1), pp. 141–147. [CrossRef]
Chen, G., Liu, X., and Du, Y., 2011, “Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges,” ASME J. Mech. Des., 133(8), p. 081002. [CrossRef]
Lobontiu, N., 2012, “Symmetry-Based Compliance Model of Multisegment Notch Flexure Hinges,” Mech. Based Des. Struct. Mach., 40(2), pp. 185–205. [CrossRef]
Chen, G., Wang, J., and Liu, X., 2014, “Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges,” ASME J. Mech. Des., 136(3), p. 031009. [CrossRef]
Zelenika, S., Munteanu, M., and De Bona, F., 2009, “Optimized Flexural Hinge Shapes for Microsystems and High-Precision Applications,” Mech. Mach. Theory, 44(10), pp. 1826–1839. [CrossRef]
Dirksen, F., Anselmann, M., Zohdi, T., and Lammering, R., 2013, “Incorporation of Flexural Hinge Fatigue-Life Cycle Criteria Into the Topological Design of Compliant Small-Scale Devices,” Precis. Eng., 37(3), pp. 531–541. [CrossRef]
Jensen, B., and Howell, L., 2002, “The Modeling of Cross-Axis Flexural Pivots,” Mech. Mach. Theory, 37(5), pp. 461–476. [CrossRef]
Shusheng, B., Hongzhe, Z., and Jingjun, Y., 2009, “Modeling of a Cartwheel Flexural Pivot,” ASME J. Mech. Des., 131(6), p. 061010. [CrossRef]
Mankame, N. D., and Ananthasuresh, G., 2004, “Topology Optimization for Synthesis of Contact-Aided Compliant Mechanisms Using Regularized Contact Modeling,” Comput. Struct., 82(15), pp. 1267–1290. [CrossRef]
Belfiore, N. P., and Simeone, P., 2013, “Inverse Kinetostatic Analysis of Compliant Four-Bar Linkages,” Mech. Mach. Theory, 69, pp. 350–372. [CrossRef]
Yong, Y. K., and Lu, T.-F., 2008, “The Effect of the Accuracies of Flexure Hinge Equations on the Output Compliances of Planar Micro-Motion Stages,” Mech. Mach. Theory, 43(3), pp. 347–363. [CrossRef]
Belfiore, N. P., Scaccia, M., Ianniello, F., and Presta, M., 2009, Selective Compliance Hinge, WO/2009/034551, International Application No. PCT/IB2008/053697, Mar. 19.
Belfiore, N., Scaccia, M., Ianniello, F., and Presta, M. P. L., 2009, Selective Compliance Wire Actuated Mobile Platform, Particularly for Endoscopiy Surgical Devices, WO/2009/034552, International Application No. PCT/IB2008/053698, Mar. 19.
Cullmann, K., 1880, Traite de Statique Graphique, Dunod, ed., Paris.
Ferrari, R., and Rizzi, E., 2008, “On the Theory of the Ellipse of Elasticity as a Natural Discretisation Method in the Design of Paderno d'adda Bridge (Italy),” Proceedings of the 6th International Conference on Structural Analysis of Historic Construction: Preserving Safety and Significance, Bath, UK, July 2–4, CRC, pp. 583–591.
Tas, N., Sonnenberg, T., Jansen, H., Legtenberg, R., and Elwenspoek, M., 1996, “Stiction in Surface Micromachining,” J. Micromech. Microeng., 6(4), p. 385. [CrossRef]
Komvopoulos, K., 1996, “Surface Engineering and Microtribology for Microelectromechanical Systems,” Wear, 200(1), pp. 305–327. [CrossRef]
Mastrangelo, C., 1997, “Adhesion-Related Failure Mechanisms in Micromechanical Devices,” Tribol. Lett., 3(3), pp. 223–238. [CrossRef]
Maboudian, R., and Howe, R. T., 1997, “Critical Review: Adhesion in Surface Micromechanical Structures,” J. Vac. Sci. Technol., B, 15(1), pp. 1–20. [CrossRef]
Rymuza, Z., 1999, “Control Tribological and Mechanical Properties of MEMS Surfaces. Part 1: Critical Review,” Microsyst. Technol., 5(4), pp. 173–180. [CrossRef]
Ashurst, W. R., Yau, C., Carraro, C., Maboudian, R., and Dugger, M. T., 2001, “Dichlorodimethylsilane as an Anti-Stiction Monolayer for MEMS: A Comparison to the Octadecyltrichlorosilane Self-Assembled Monolayer,” J. Microelectromech. Syst., 10(1), pp. 41–49. [CrossRef]
Ashurst, W. R., Yau, C., Carraro, C., Lee, C., Kluth, G. J., Howe, R. T., and Maboudian, R., 2001, “Alkene Based Monolayer Films as Anti-Stiction Coatings for Polysilicon MEMS,” Sens. Actuators, A, 91(3), pp. 239–248. [CrossRef]
van Spengen, W. M., Wijts, G. H. C. J., Turq, V., and Frenken, J. W. M., 2010, “Microscale Friction Reduction by Normal Force Modulation in MEMS,” J. Adhes. Sci. Technol., 24(15–16), pp. 2669–2680. [CrossRef]
Belfiore, N., Verotti, M., and Consorti, L., 2010, “Comparative Analysis of Isotropy Indices in RR and RRP Arms,” Int. J. Mech. Control, 11(1), pp. 3–12.
Belfiore, N., Di Giamberardino, P., Rudas, I., and Verotti, M., 2011, “Isotropy in Any RR Planar Dyad Under Active Joint Stiffness Regulation,” Int. J. Mech. Control, 12(1), pp. 75–81.
Belfiore, N. P., Verotti, M., Di Giamberardino, P., and Rudas, I. J., 2012, “Active Joint Stiffness Regulation to Achieve Isotropic Compliance in the Euclidean Space,” J. Mech. Rob., 4(4), p. 041010. [CrossRef]
Petersen, K. E., 1982, “Silicon as a Mechanical Material,” Proc. IEEE, 70(5), pp. 420–457. [CrossRef]
Hopcroft, M. A., Nix, W. D., and Kenny, T. W., 2010, “What Is the Young's Modulus of Silicon?,” J. Microelectromech. Syst., 19(2), pp. 229–238. [CrossRef]
Kota, S., Joo, J., Li, Z., Rodgers, S., and Sniegowski, J., 2001, “Design of Compliant Mechanisms: Applications to MEMS,” Analog Integr. Circuits Signal Process., 29(1), pp. 7–15. [CrossRef]
Howell, L., Midha, A., and Norton, T., 1996, “Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms,” ASME J. Mech. Des., 118(1), pp. 126–131. [CrossRef]
Belfiore, N. P., 2014, “Functional Synthesis of a New Class of Micro Electro-Mechanical Systems,” Advances in Soft Computing, Intelligent Robotics and Control. Vol. 8 (Topics in Intelligent Engineering and Informatics), Springer International Publishing, pp. 81–93.
Freudenstein, F., Bottema, O., and Koetsier, M., 1969, “Finite Conic-Section Burmester Theory,” J. Mech., 4(4), pp. 359–373. [CrossRef]
Belfiore, N. P., Prosperi, G., and Crescenzi, R., 2014, “A Simple Application of Conjugate Profile Theory to the Development of a Silicon Micro Tribometer,” Proceedings of ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis, ASME, Copenhagen, Denmark, July 25–27.
Balucani, M., Belfiore, N. P., Crescenzi, R., and Verotti, M., 2011, “The Development of a MEMS/NEMS-Based 3 D.O.F. Compliant Micro Robot,” Int. J. Mech. Control, 12(1), pp. 3–10.
Chang, S.-L., and Tsai, L.-W., 1990, “On the Redundant - Drive Backlash - Free Robotic Mechanisms,” ASME J. Mech. Des.115(2), pp. 247–254.
Nemeth, N., Evans, L., Jadaan, O., Sharpe, W., Beheim, G., and Trapp, M., 2007, “Fabrication and Probabilistic Fracture Strength Prediction of High-Aspect-Ratio Single Crystal Silicon Carbide Microspecimens With Stress Concentration,” Thin Solid Films, 515(6), pp. 3283–3290. [CrossRef]
Merlijn Van Spengen, W., 2012, “Static Crack Growth and Fatigue Modeling for Silicon MEMS,” Sens. Actuators, A, 183, pp. 57–68. [CrossRef]


Grahic Jump Location
Fig. 1

Geometry of the CSFH: configuration A (Fig. 1(a)) and configuration B (Fig. 1(b))

Grahic Jump Location
Fig. 2

PVC foam board CSFH (B-type) in its neutral and deformed configurations

Grahic Jump Location
Fig. 3

Deflection of a curved beam with nomenclature

Grahic Jump Location
Fig. 4

Static balance and nomenclature

Grahic Jump Location
Fig. 5

von Mises equivalent stress distribution (MPa)

Grahic Jump Location
Fig. 6

Contact simulation: geometric parameters and load conditions

Grahic Jump Location
Fig. 7

Mesh for the contact simulation

Grahic Jump Location
Fig. 8

von Mises equivalent stress distribution in case of contact between the conjugate surfaces

Grahic Jump Location
Fig. 9

von Mises equivalent stress distribution in case of penetration of the conjugate surfaces

Grahic Jump Location
Fig. 10

Maximum values of von Mises equivalent stress in case of surfaces in contact (solid line) and in case of penetration (dotted line). The dashed-dotted line represents, for each value of the force magnitude, the maximum value of the contact pressure.

Grahic Jump Location
Fig. 11

Rigid-body four-bar linkage (Fig. 11(a)) and corresponding compliant four-bar linkage designed with CSFHs (Fig. 11(b))

Grahic Jump Location
Fig. 12

Displacements of the four-bar linkage under the action of a concentrated vertical force

Grahic Jump Location
Fig. 13

Contact pressure within the four pairs of conjugate surfaces embedded in the four-bar linkage under the action of a concentrated vertical force

Grahic Jump Location
Fig. 14

Relative sliding among the 4 pairs of conjugate surfaces embedded in the four-bar linkage under the action of a concentrated vertical force

Grahic Jump Location
Fig. 15

Rigid-body six-bar Stevenson linkage (Fig. 15(a)) and corresponding compliant mechanisms designed with CSFHs (Fig. 15(b))

Grahic Jump Location
Fig. 16

Rigid-body six-bar Watt linkage (Fig. 16(a)) and corresponding compliant mechanism designed with CSFHs (Fig. 16(b))

Grahic Jump Location
Fig. 17

Compliant microstage and corresponding six-bar PRBM

Grahic Jump Location
Fig. 18

The process phases adopted for the Si–prototypes

Grahic Jump Location
Fig. 19

Two samples of silicon prototypes

Grahic Jump Location
Fig. 20

A sequence of SEM image frames showing the motion of the platform due to the application of an incremental load

Grahic Jump Location
Fig. 21

Video tracking performed after the SEM experiment

Grahic Jump Location
Fig. 22

SEM Image of the real curved beam with stress concentrated regions




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In