Torsional Rigidity of a Two-stage Cycloid Drive

이단 사이클로이드 드라이브의 비틀림 강성

  • 김경홍 (숭실대학교 대학원 기계공학과) ;
  • 이춘세 (숭실대학교 대학원 기계공학과) ;
  • 안형준 (숭실대학교 기계공학과)
  • Published : 2009.11.01


This paper presents a finite element (FE) analysis of the torsional rigidity of a two-stage cycloid drive. The cycloid disk makes contact with a number of pin-rollers simultaneously and eccentric shafts transmit not only torque of the spur gear stage to the cycloid disk, but also that of the cycloid disk to the output disk. Contacts between the disk and pin-rollers are simplified as linear spring elements, and the bearing of eccentric shaft is modeled as a rigid ring that has frictional contact to the disk and an elastic support. FE analysis for an ideal solid cycloid drive was performed and verified by a theoretical calculation. Accurate contact forces were then estimated by iterating between FE analysis for contact forces and Hertz theory calculations for nonlinear contact stiffness. In addition, torsional rigidity of the cycloid drive is analyzed to show that the bearing and nonlinear Hertz contact theory should be considered in analysis and design of a cycloid drive, which was verified with experiments. Finally, the effects of contact stiffness, bearing stiffness and cycloid disk structural stiffness according to the cycloid disk rotation on the torsional rigidity were investigated.


Cycloid Drive;FE Analysis;Hertz Contact Theory;Torsional Rigidity


  1. Botsiber, D.W., Kingston, L., 1956, 'Design and Performance of the Cycloid Speed Reducer,' Machine Design, pp. 65-69
  2. Nabtesco, 2005, 'RV-E series catalog'
  3. Malhotra, S.K., Parameswaran, M.A., 1983, 'Analysis of a Cycloid Speed Reducer,' Mechanism and Machine Theory, Vol. 18, No. 6, pp. 491-499
  4. Lee, S. C., Oh, P. K., Kwon, O. K., 1987, 'A Study on the Design of Planocentric Torque Driver Used in Industrial Robot,' Journal of the KSLE, Vol. 3, No. 2, pp. 72-80
  5. Nam, W. K., Jang, I. H., Oh, S. H., Sim, K.B., 2006, 'Development and Design of Robot Speed Reducer(RSR) with Straight Line Teeth Profile for Human Robot,' Journal of the KIIS, Vol . 16, No. 3, pp. 315-320
  6. Ishida, T., Hidaka, T., Wang, H., Yamada, H. and Hashimoto, M., 1996, 'Bending Stress and Tooth Contact Stress of Cycloid Gear with Thin Rims,' Transactions of the JSME C, Vol. 62, No. 593, pp. 291-297
  7. Ishida, T., Shuting, Li. Yoshida, T., 1996, 'Tooth Load of Thin Rim Cycloidal Gear,' Power Transmission and Gearing Conference, ASME, DE-Vol. 88
  8. Park, J. S., 2006, 'Stiffness and Error Analysis of the Cycloid Drive,' Ph.D Thesis, School of Mechanical and Aerospace Engineering at Seoul National University
  9. Park, J. S., Lee, S. Y., Ahn, H. J., Han, D. C., 2005, 'Analysis of the Cycloid Drive with Tolerances,' Proc. of KSME autumn conference, pp. 2480-2484
  10. Lee, S. Y., Park, J. S., Ahn, H. J.,, Han, D. C., 2005, 'Torsional Stiffness Analysis of a Cycloid Reducer Using Hertz Contact Theory,' Proc. of KSPE autumn conference, pp. 816-821
  11. Kim, K. H., Lee, C. S., Ahn, H. J., 2008, 'Torsional Stiffness of Cycloid Gear Considering Bearing and Hertz Contact,' Proc. of KSPE autumn conference, pp. 61-62
  12. BEARINX(R)-online Shaft Calculation, INA-Schaeffler KG, 91072 Herzogenaurach (Germany)
  13. Johnson, K.L., 2001, Contact Mechanics, Cambridge University Press
  14. Shin, J. H., Yoon, H. E., Kang, D. W., 2001, 'Study on Shape Design Method of Cycloidal Plate Gear,' Journal(A) of the KSME, Vol. 25, No. 1, pp. 70-80