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A novel method to generate the geometry of a surface actuator

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This paper presents the design, evaluation, and implementation of a continuous surface actuator. A surface actuator as a shape-changing interface can facilitate the modeling process in interactive product design approaches by rendering products in 3D space for better understanding and visualization. Controlling the deformation of a continuous tactile surface using a pneumatic air pressure mechanism holds promise as a tangible haptic interface. Previous haptic actuators could only provide physical point contact with the user’s hand. In this article, a three-dimensional (3D) surface is produced to simulate the shape of a desired continuous object. To investigate the mechanical behavior of this deformable surface, the hyperelastic Yeoh model is employed to numerically simulate the experimental system behavior. The parameters of the hyperelastic material have been characterized by a tensile test. An experimental setup is developed to produce an arbitrary spherical shape containing specific deformations. For validation purposes, the surface shape has been scanned and compared with the finite element simulation results.

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  1. 1.

    In encountered-type haptic displays, a user can freely and directly interact and explore the surface of the display.

  2. 2.

    Two perpendicular directions.

  3. 3.

    Abaqus is a software suite for finite element analysis and computer-aided engineering.

  4. 4.

    Encastre boundary condition fixes both the displacements and the rotations of a desired region.

  5. 5.

    Pinning boundary condition only fixes the displacements of a desired region.


  1. 1.

    Davaria, S., Najafi, F., Mahjoob, M.J., Motahari-Bidgoli, S.M.: Design and fabrication of a robotic tactile device for abdominal palpation. In: 2014 Second RSI/ISM International Conference on Robotics and Mechatronics (ICRoM), vol. 68, no. 5, pp. 339–344 (2014)

  2. 2.

    Herzig, N., Maiolino, P., Iida, F., Nanayakkara, T.: A variable stiffness robotic probe for soft tissue palpation. IEEE Robot. Autom. Lett. 3(2), 1168–1175 (2018)

  3. 3.

    Najafi, F., Sepehri, N.: A robotic wrist for remote ultrasound imaging. Mech. Mach. Theory 46(8), 1153–1170 (2011)

  4. 4.

    Najafi, F., Sepehri, N.: A novel hand-controller for remote ultrasound imaging. Mechatronics 18(10), 578–590 (2008)

  5. 5.

    Bordegoni, M., Cugini, U.: Haptic modeling in the conceptual phases of product design. Virtual Real. 9(2–3), 192–202 (2006)

  6. 6.

    Wang, Z., Dumont, G.: Haptic manipulation of deformable CAD parts with a two-stage method. Int. J. Interact. Des. Manuf. 5(4), 255–270 (2011)

  7. 7.

    Perret, J., Kneschke, C., Vance, J., Dumont, G.: Interactive assembly simulation with haptic feedback. Assem. Autom. 33(3), 214–220 (2013)

  8. 8.

    Arbeláez, J.C., Viganò, R., Osorio-Gómez, G.: Haptic augmented reality (HapticAR) for assembly guidance. Int. J. Interact. Des. Manuf. 13(2), 673–687 (2019)

  9. 9.

    Ishii, H., Ullmer, B.: Tangible bits: towards seamless interfaces between people, bits, and atoms. In: Proceedings of the 8th International Conference on Intelligent User Interfaces, pp. 3–3 (1997)

  10. 10.

    Stanley, A.A., Okamura, A.M.: Deformable model-based methods for shape control of a haptic jamming surface. IEEE Trans. Vis. Comput. Graph. 23(2), 1029–1041 (2017)

  11. 11.

    Stanley, A.A., Gwilliam, J.C., Okamura, A.M.: Haptic jamming: a deformable geometry, variable stiffness tactile display using pneumatics and particle jamming. In: 2013 World Haptics Conference, WHC 2013, pp. 25–30 (2013)

  12. 12.

    Rossignac, J., et al.: Finger sculpting with Digital Clay: 3D shape input and output through a computer-controlled real surface. In: 2003 Shape Modeling International, vol. 2003, pp. 229–231 (2003)

  13. 13.

    Zhu, H., Book, W.J.: Control concepts for digital clay. IFAC Proc. 36(17), 347–352 (2003)

  14. 14.

    Iwata, H., Yano, H., Ono, N.: Volflex. In: ACM SIGGRAPH 2005 Emerging technologies on—SIGGRAPH’05, p. 31 (2005)

  15. 15.

    Follmer, S., Leithinger, D., Olwal, A., Hogge, A., Ishii, H.: inFORM: dynamic physical affordances and constraints through shape and object actuation. UIST 13, 417–426 (2013)

  16. 16.

    Schoessler, P., Windham, D., Leithinger, D., Follmer, S., Ishii, H.: Kinetic blocks. In: Proceedings of the 28th Annual ACM Symposium on User Interface Software and Technology—UIST’15, pp. 341–349 (2015)

  17. 17.

    Nakagaki, K., et al.: Materiable. In: Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems—CHI’16, pp. 2764–2772 (2016)

  18. 18.

    Abtahi, P., Follmer, S.: Visuo-haptic illusions for improving the perceived performance of shape displays. In: Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems—CHI’18, pp. 1–13 (2018)

  19. 19.

    Lee, J.M., Wagner, C.R., Lederman, S.J., Howe, R.D.: Spatial low pass filters for pin actuated tactile displays. In: 11th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, HAPTICS 2003. Proceedings, pp. 57–62 (2003)

  20. 20.

    Howe, R.D., Peine, W.J., Kontarinis, D.A., Son, J.S.: Remote palpation technology. IEEE Eng. Med. Biol. Mag. 14(3), 318–323 (1995)

  21. 21.

    Najmaei, N., Asadian, A., Kermani, M.R., Patel, R.V.: Magneto-rheological actuators for haptic devices: design, modeling, control, and validation of a prototype clutch. In: 2015 IEEE International Conference on Robotics and Automation (ICRA), vol. 2015-June, no. June, pp. 207–212 (2015)

  22. 22.

    Taylor, P.M., Pollet, D.M., Hosseini-Sianaki, A., Varley, C.J.: Advances in an electrorheological fluid based tactile array. Displays 18(3), 135–141 (1998)

  23. 23.

    Manti, M., Cacucciolo, V., Cianchetti, M.: Stiffening in soft robotics : a review of the state of the art stiffening in soft robotics: a review. (2016)

  24. 24.

    Ogden, R.: Non-linear elastic deformations. Eng. Anal. Bound. Elem. 1(2), 119 (1984)

  25. 25.

    Yeoh, O.H.: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66(5), 754–771 (1993)

  26. 26.

    Martins, P.A.L.S., Jorge, R.M.N., Ferreira, A.J.M.: A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues. Strain 42(3), 135–147 (2006)

  27. 27.

    Treloar, L.R.G.: The mechanics of rubber elasticity. Proc. R. Soc. A Math. Phys. Eng. Sci. 260(107–123), 459–474 (1961)

  28. 28.

    Stanley, A.A., Okamura, A.M.: Controllable surface haptics via particle jamming and pneumatics. IEEE Trans. Haptics 8(1), 20–30 (2015)

  29. 29.

    Genecov, A.M., Stanley, A.A., Okamura, A.M.: Perception of a haptic jamming display: just noticeable differences in stiffness and geometry. In: 2014 IEEE Haptics Symposium (HAPTICS), pp. 333–338 (2014)

  30. 30.

    Charlton, D.J., Yang, J., Teh, K.K.: A review of methods to characterize rubber elastic behavior for use in finite element analysis. Rubber Chem. Technol. 67(3), 481–503 (1994)

  31. 31.

    Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11(9), 582–592 (1940)

  32. 32.

    Zimm, B.H., Kilb, R.W.: The physics of rubber elasticity. J. Phys. Chem. Solids 9(3–4), 338 (1959)

  33. 33.

    Ogden, R.W.: Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. A Math. Phys. Eng. Sci. 326(1567), 565–584 (1972)

  34. 34.

    Holzapfel, G.A.: Nonlinear solid mechanics: a continuum approach for engineering science. Meccanica 37(4), 489–490 (2002)

  35. 35.

    Bustos, C., Herrera, C.G., Celentano, D., Chen, D., Cruchaga, M.: Numerical simulation and experimental validation of the inflation test of latex balloons. Lat. Am. J. Solids Struct. 13(14), 2357–2378 (2016)

  36. 36.

    Girardeau-Montaut, D.: Cloudcompare-open source project. In: OpenSource Proj. (2011)

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Correspondence to Farshid Najafi.

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Khalghollah, M., Nayyeri, P. & Najafi, F. A novel method to generate the geometry of a surface actuator. Int J Interact Des Manuf 14, 211–223 (2020). https://doi.org/10.1007/s12008-020-00656-x

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  • Shape-changing interface
  • Continuous haptic display
  • Hyperelastic model
  • Numerical simulation
  • Experimental validation