Structural Engineering and Mechanics

  • 제82권4호
  • /
  • Pages.503-515
  • /
  • 2022
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Enhanced generalized modeling method for compliant mechanisms: Multi-Compliant-Body matrix method

  • Lim, Hyunho (Department of Mechanical Engineering, Ajou University) ;
  • Choi, Young-Man (Department of Mechanical Engineering, Ajou University)
  • 투고 : 2021.11.30
  • 심사 : 2022.02.16
  • 발행 : 2022.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

The multi-rigid-body matrix method (MRBMM) is a generalized modeling method for obtaining the displacements, forces, and dynamic characteristics of a compliant mechanism without performing inner-force analysis. The method discretizes a compliant mechanism of any type into flexure hinges and rigid bodies by implementing a multi-body mass-spring model using coordinate transformations in a matrix form. However, in this method, the deformations of bodies that are assumed to be rigid are inherently omitted. Consequently, it may yield erroneous results in certain mechanisms. In this paper, we present a multi-compliant-body matrix-method (MCBMM) that considers a rigid body as a compliant element, while retaining the generalized framework of the MRBMM. In the MCBMM, a rigid body in the MRBMM is segmented into a certain number of body nodes and flexure hinges. The proposed method was verified using two examples: the first (an XY positioning stage) demonstrated that the MCBMM outperforms the MRBMM in estimating the static deformation and dynamic mode. In the second example (a bridge-type displacement amplification mechanism), the MCBMM estimated the displacement amplification ratio more accurately than several previously proposed modeling methods.

키워드

과제정보

This research was supported by Ajou University and by the Technology Innovation Program, No. 20014812, funded by the Ministry of Trade, Industry & Energy (MOTIE, Republic of Korea).

참고문헌

  1. Chen, S., Wan, H., Jiang, C., Ye, L., Yu, H., Yang, M., Zhang, C., Yang, G. and Wu, J. (2021), "Kinetostatic modeling of dual-drive H-Type gantry with exchangeable flexure joints", J. Mech. Robot., 13(4), 40908. https://doi.org/10.1115/1.4050830.
  2. Choi, K.B., Lee, J.J., Kim, G.H., Lim, H.J. and Kwon, S.G. (2018), "Amplification ratio analysis of a bridge-type mechanical amplification mechanism based on a fully compliant model", Mech. Mach. Theory, 121, 355-372. https://doi.org/10.1016/j.mechmachtheory.2017.11.002.
  3. Darnieder, M., Pabst, M., Wenig, R., Zentner, L., Theska, R. and Frohlich, T. (2018), "Static behavior of weighing cells", J. Sensor. Sensor Syst., 7(2), 587-600. https://doi.org/10.5194/jsss7-587-2018.
  4. Dearden, J., Grames, C., Jensen, B.D., Magleby, S.P. and Howell, L.L. (2017), "Inverted L-arm gripper compliant mechanism", J. Med. Dev., Trans. ASME, 11(3), 034502. https://doi.org/10.1115/1.4036336.
  5. Hong, M.B. and Jo, Y.H. (2012), "Design and evaluation of 2-DOF compliant forceps with force-sensing capability for minimally invasive robot surgery", IEEE Tran. Robot., 28(4), 932-941. https://doi.org/10.1109/TRO.2012.2194889.
  6. Iqbal, S. and Malik, A. (2019), "A review on MEMS based micro displacement amplification mechanisms", Sensor. Actuat., A: Phys., 300, 111666. https://doi.org/10.1016/j.sna.2019.111666.
  7. Kahr, M., Steiner, H., Hortschitz, W., Stifter, M., Kainz, A. and Keplinger, F. (2018), "3D-Printed MEMS magnetometer featuring compliant mechanism", Proceed., 2(13), 784. https://doi.org/10.3390/proceedings2130784.
  8. Kim, J.H., Kim, S.H. and Kwaka, Y.K. (2003), "Development of a piezoelectric actuator using a three-dimensional bridge-type hinge mechanism", Rev. Scientif. Instrum., 74(5), 2918-2924. https://doi.org/10.1063/1.1569411.
  9. Kim, K., Ahn, D. and Gweon, D. (2012), "Optimal design of a 1-rotational DOF flexure joint for a 3-DOF H-type stage", Mechatron., 22(1), 24-32. https://doi.org/10.1016/j.mechatronics.2011.10.002.
  10. Koseki, Y., Tanikawa, T., Arai, T. and Koyachi, N. (2002), "Kinematic analysis of translational 3-DOF micro parallel mechanism using matrix method", Adv. Robot., 16(3), 251-264. https://doi.org/10.1163/156855302760121927.
  11. Kumar, P., Ghyar, R. and Ravi, B. (2020), "Topology optimization of compliant mechanism for laparoscopic surgery instruments", ACM International Conference Proceeding Series, October.
  12. Lee, H.J., Kim, H.C., Kim, H.Y. and Gweon, D.G. (2013), "Optimal design and experiment of a three-axis out-of-plane nano positioning stage using a new compact bridge-type displacement amplifier", Rev. Scientif. Instrum., 84(11), 115103. https://doi.org/10.1063/1.4827087.
  13. Lee, H.J., Woo, S., Park, J., Jeong, J.H., Kim, M., Ryu, J., Gweon, D.G. and Choi, Y.M. (2018), "Compact compliant parallel XY nano-positioning stage with high dynamic performance, small crosstalk, and small yaw motion", Microsyst. Technol., 24(6), 2653-2662. https://doi.org/10.1007/s00542-017-3626-z.
  14. Li, H., Duan, X., Li, G., Oldham, K.R. and Wang, T.D. (2017), "An electrostatic MEMS translational scanner with large out-of-plane stroke for remote axial-scanning in multi-photon microscopy", Micromach., 8(5), 159. https://doi.org/10.3390/mi8050159.
  15. Lin, C., Shen, Z., Wu, Z. and Yu, J. (2018), "Kinematic characteristic analysis of a micro-/nano positioning stage based on bridge-type amplifier", Sensor. Actuator., A: Phys., 271, 230-242. https://doi.org/10.1016/J.SNA.2017.12.030.
  16. Ling, M., Cao, J. and Pehrson, N. (2019), "Kinetostatic and dynamic analyses of planar compliant mechanisms via a two-port dynamic stiffness model", Precis. Eng., 57, 149-161. https://doi.org/10.1016/j.precisioneng.2019.04.004.
  17. Ling, M., Cao, J., Howell, L.L. and Zeng, M. (2018a), "Kinetostatic modeling of complex compliant mechanisms with serial-parallel substructures: A semi-analytical matrix displacement method", Mech. Mach. Theory, 125, 169-184. https://doi.org/10.1016/j.mechmachtheory.2018.03.014.
  18. Ling, M., Cao, J., Jiang, Z. and Lin, J. (2017), "Modular kinematics and statics modeling for precision positioning stage", Mech. Mach. Theory, 107, 274-282. https://doi.org/10.1016/j.mechmachtheory.2016.10.009.
  19. Ling, M., Cao, J., Jiang, Z. and Lin, J. (2018b), "A semi-analytical modeling method for the static and dynamic analysis of complex compliant mechanism", Precis. Eng., 52, 64-72. https://doi.org/10.1016/10.1016/j.precisioneng.2017.11.008.
  20. Ling, M., Cao, J., Zeng, M., Lin, J. and Inman, D.J. (2016), "Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms", Smart Mater. Struct., 25(7), 075022. https://doi.org/10.1088/0964-1726/25/7/075022.
  21. Ling, M., Howell, L.L., Cao, J. and Chen, G. (2020), "Kinetostatic and dynamic modeling of flexure-based compliant mechanisms: A survey", Appl. Mech. Rev., 72(3), 030802. https://doi.org/10.1115/1.4045679.
  22. Ling, M., Howell, L.L., Cao, J. and Jiang, Z. (2018c), "A pseudo-static model for dynamic analysis on frequency domain of distributed compliant mechanisms", J. Mech. Robot., 10(5), 051011. https://doi.org/10.1115/1.4040700.
  23. Lobontiu, N. (2014), "Compliance-based matrix method for modeling the quasi-static response of planar serial flexure-hinge mechanisms", Precis. Eng., 38(3), 639-650. https://doi.org/10.1016/j.precisioneng.2014.02.014.
  24. Lobontiu, N. and Garcia, E. (2003), "Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms", Comput. Struct., 81(32), 2797-2810. https://doi.org/10.1016/j.compstruc.2003.07.003.
  25. Lobontiu, N. and Garcia, E. (2004), "Static response of planar compliant devices with small-deformation flexure hinges", Mech. Bas. Des. Struct. Mach., 32(4), 459-490. https://doi.org/10.1081/SME-200034157.
  26. Ma, H.W., Yao, S.M., Wang, L.Q. and Zhong, Z. (2006), "Analysis of the displacement amplification ratio of bridge-type flexure hinge", Sensor. Actuator., 132(2), 730-736. https://doi.org/10.1016/j.sna.2005.12.028.
  27. Marangoni, R.R., Rahneberg, I., Hilbrunner, F., Theska, R. and Frohlich, T. (2017), "Analysis of weighing cells based on the principle of electromagnetic force compensation", Measure. Sci. Technol., 28(7), 075101. https://doi.org/10.1088/1361-6501/aa6bcd.
  28. Meng, Q., Li, Y. and Xu, J. (2014), "A novel analytical model for flexure-based proportion compliant mechanisms", Precis. Eng., 38(3), 449-457. https://doi.org/10.1016/j.precisioneng.2013.12.001.
  29. Milojevic, A., Lins, S. and Handroos, H. (2021), "Soft robotic compliant two-finger gripper mechanism for adaptive and gentle food handling", IEEE 4th International Conference on Soft Robotics, April.
  30. Pham, H.H. and Chen, I.M. (2005), "Stiffness modeling of flexure parallel mechanism", Precis. Eng., 29(4), 467-478. https://doi.org/10.1016/j.precisioneng.2004.12.006.
  31. Pohlmann, P., Peukert, C., Merx, M., Muller, J. and Ihlenfeldt, S. (2020), "Compliant joints for the improvement of the dynamic behaviour of a gantry stage with direct drives", J. Mach. Eng., 20(3), 17-29. https://doi.org/10.36897/jme/127103.
  32. Qin, Y., Shirinzadeh, B., Tian, Y., Zhang, D. and Bhagat, U. (2014), "Design and computational optimization of a decoupled 2-DOF monolithic mechanism", IEEE/ASME Trans. Mechatron., 19(3), 872-881. https://doi.org/10.1109/TMECH.2013.2262801.
  33. Ryu, J.W., Gweon, D.G. and Moont, K.S. (1997), "Optimal design of a flexure hinge based XY0 wafer stage", Precis. Eng., 21(1), 18-28. http://doi.org/10.1016/s0141-6359(97)00064-0.
  34. Sun, Y., Zhang, D., Liu, Y. and Lueth, T.C. (2020), "FEM-based mechanics modeling of bio-inspired compliant mechanisms for medical applications", IEEE Trans. Med. Robot. Bionic., 2(3), 364-373. http://doi.org/10.1101/2020.06.15.151670.
  35. Tang, H. and Li, Y. (2012), "Optimal design of the lever displacement amplifiers for a flexure-based dual-mode motion stage", IEEE/ASME International Conference on Advanced Intelligent Mechatronics, July.
  36. Tang, H. and Li, Y. (2014), "Development and active disturbance rejection control of a compliant micro-/nanopositioning piezostage with dual mode", IEEE Trans. Indus. Electron., 61(3), 1475-1492. http://doi.org/10.1109/TIE.2013.2258305.
  37. Tian, Y., Lu, K., Wang, F., Zhou, C., Ma, Y., Jing, X., Yang, C. and Zhang, D. (2020), "A spatial deployable three-DOF compliant nano-positioner with a three-stage motion amplification mechanism", IEEE/ASME Trans. Mechatron., 25(3), 1322-1334. http://doi.org/10.1109/TMECH.2020.2973175.
  38. Tian, Y., Shirinzadeh, B. and Zhang, D. (2010), "Design and dynamics of a 3-DOF flexure-based parallel mechanism for micro/nano manipulation", Microelectron. Eng., 87(2), 230-241. https://doi.org/10.1016/j.mee.2009.08.001.
  39. Wang, F., Zhao, X., Huo, Z., Shi, B., Liang, C., Tian, Y. and Zhang, D. (2021), "A 2-DOF nano-positioning scanner with novel compound decoupling-guiding mechanism", Mech. Mach. Theory, 155, 104066. http://doi.org/10.1016/j.mechmachtheory.2020.104066.
  40. Xu, Q. and Li, Y. (2011), "Analytical modeling, optimization and testing of a compound bridge-type compliant displacement amplifier", Mech. Mach. Theory, 46(2), 183-200. https://doi.org/10.1016/j.mechmachtheory.2010.09.007.
  41. Yang, J., Kim, J., Kim, D. and Yun, D. (2021), "Shock resistive flexure-based anthropomorphic hand with enhanced payload", Soft Robot., 9(2), 266-279. https://doi.org/10.1089/soro.2020.0067.