Skip to main content
SpringerLink
Log in

Lost motion analysis of one stage cycloid reducer considering tolerances

  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

Cycloid reducers have a high reduction ratio, high efficiency, high stiffness and are a compact size, compared to conventional reducer mechanisms, so that they are attractive candidates for limited space and precision applications such as industrial robots and cars. However, the integrated performance of torsional stiffness and backlash or lost motion has not been studied yet. This paper investigates the lost motion of a cycloid reducer combining FE and kinematic analyses. First, we introduce the cycloid reducer and its hysteresis curve. Next, a kinematic analysis of the cycloid reducer is performed considering tolerance. Then, an iterative FE analysis of the lost motion of the cycloid reducer is performed combining the results of the kinematic analysis. We conclude that the lost motion of the cycloid reducer depends on not only its torsional stiffness but also its tolerance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a i :

Width of contact area

b :

Thickness of the cycloid disk

e :

Eccentricity

E :

Young’s modulus of material

E*:

Equivalent Young’s modulus

F 1i :

Contact force

g j :

Gap between cycloid disk and pin-roller j th

k p :

Initial stiffness of pin-roller

k i :

Hertz contact stiffness of pin roller i th

N :

Reduction ratio of cycloid reducer

R h :

Radius of housing

R i :

Radius of curvature (+ convex, − concave)

R * i :

Equivalent radius of curvature

Rr:

Radius of pin roller

x Ci , y Ci :

Coordinates of point i th at φ i of cycloid profile

x Zj , y Zj :

Coordinates of the center of j th pin-roller

Z i :

Center of ith pin-roller

Z i :

Center of i th pin-roller

ν :

Poisson ratio of material

ΔR h :

Tolerance at cycloid disk

ΔR r :

Tolerance at pin-roller

β :

Backlash angle

ε :

Surface roughness of cycloid disk

θ bj :

Angle between O g Z i and vertical direction

θ o0 :

Initial position of output

θ oi :

Position of output shaft

θ in :

Position of input shaft

References

  1. PwC, “The New Hire: How a New Generation of Robots is Transforming Manufacturing,” http://www.pwc.com/us/en/industrialproducts/ next-manufacturing/robotic-trends-changing-manufacturing. html (Accessed 26 MAY 2016)

    Google Scholar 

  2. Warnecke, I. H. and Schiele, D.-I. G., “Performance Characteristics and Performance Testing of Industrial Robots -State of the Art,” in: Robot Technology and Applications, Rathmill, K., MacConaill, P., O’Leary, P., and Browne, J., (Eds.), Springer, pp. 5–17, 1985.

    Chapter  Google Scholar 

  3. Harmonic Drive, “Improve the Productivity of Your Factory Automation Systems with Lightweight Gears and Actuators,” http:// www.harmonicdrive.net/whitepapers/improve-the-productivity-ofyour-factory-automation-systems-with-lightweight-gears-andactuators (Accessed 26 MAY 2016)

    Google Scholar 

  4. Nabtesco, “Precision Reduction Gear RV-E Series/C Series/Original Series,” http://www.nabtescomotioncontrol.com/pdfs/rv-e-c-series. pdf (Accessed 27 JUN 2016)

    Google Scholar 

  5. Yanabe, S., Ishizuka, S., Yamaguchi, T., and Ikeda, M., “Torsional Stiffness of Harmonic Drive Reducers,” Transactions of the Japan Society of Mechanical Engineers -Part C, Vol. 55, No. 509, pp. 216–221, 1989.

    Article  Google Scholar 

  6. Kircanski, N. M. and Goldenberg, A. A., “An Experimental Study of Nonlinear Stiffness, Hysteresis, and Friction Effects in Robot Joints with Harmonic Drives and Torque Sensors,” The International Journal of Robotics Research, Vol. 16, No. 2, pp. 214–239, 1997.

    Article  Google Scholar 

  7. Taghirad, H. D. and Belanger, P. R., “Modeling and Parameter Identification of Harmonic Drive Systems,” Journal of Dynamic Systems, Measurement, and Control, Vol. 120, No. 4, pp. 439–444, 1998.

    Article  Google Scholar 

  8. Tjahjowidodo, T., Al-Bender, F., and Van Brussel, H., “Theoretical Modelling and Experimental Identification of Nonlinear Torsional Behaviour in Harmonic Drives,” Mechatronics, Vol. 23, No. 5, pp. 497–504, 2013.

    Article  Google Scholar 

  9. Dhaouadi, R., Ghorbel, F. H., and Gandhi, P. S., “A New Dynamic Model of Hysteresis in Harmonic Drives,” IEEE Transactions on Industrial Electronics, Vol. 50, No. 6, pp. 1165–1171, 2003.

    Article  Google Scholar 

  10. Zhang, H., Ahmad, S., and Liu, G., “Modeling of Torsional Compliance and Hysteresis Behaviors in Harmonic Drives,” IEEE/ ASME Transactions on Mechatronics, Vol. 20, No. 1, pp. 178–185, 2015.

    Article  Google Scholar 

  11. Blanche, J. G. and Yang, D. C. H., “Cycloid Drives with Machining Tolerances,” Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 111, No. 3, pp. 337–344, 1989.

    Article  Google Scholar 

  12. Yang, D. C. H. and Blanche, J. G., “Design and Application Guidelines for Cycloid Drives with Machining Tolerances,” Mechanism and Machine Theory, Vol. 25, No. 5, pp. 487–501, 1990.

    Article  Google Scholar 

  13. Blagojeviæ, M., “Analysis of Clearances and Deformations at Cycloid Disc,” Machine Design, Vol. 6, No. 3, pp. 79–84, 2014.

    Google Scholar 

  14. Zhang, J., Chen, B., and Lyu, S.-K., “Mathematical Model and Analysis on Cycloid Planetary Gear,” Proc. of 2nd International Conference on Mechanic Automation and Control Engineering (MACE), pp. 400–403, 2011.

    Google Scholar 

  15. Meng, Y., Wu, C., and Ling, L., “Mathematical Modeling of the Transmission Performance of 2k-H Pin Cycloid Planetary Mechanism,” Mechanism and Machine Theory, Vol. 42, No. 7, pp. 776–790, 2007.

    Article  MATH  Google Scholar 

  16. Kim, K.-H., Lee, C.-S., and Ahn, H.-J., “Torsional Rigidity of a Cycloid Drive Considering Finite Bearing and Hertz Contact Stiffness,” Proc. of ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 125–130, 2009.

    Google Scholar 

  17. Shin, J.-H. and Kwon, S.-M., “On the Lobe Profile Design in a Cycloid Reducer using Instant Velocity Center,” Mechanism and Machine Theory, Vol. 41, No. 5, pp. 596–616, 2006.

    Article  MATH  Google Scholar 

  18. Ishida, T., Li, S., Yoshida, Y., and Hidaka, T., “Tooth Load of Thin Rim Cycloidal Gear,” Proc. of 7th ASME International Power Transmission and Gearing Conference, DE-Vol. 88, pp. 565–571, 1996.

    Google Scholar 

  19. Johnson, K. L., “Contact Mechanics,” Cambridge University Press, pp. 84–106, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Graduate School, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul, 34056, South Korea

    The Linh Tran

  2. Department of Convergence Software, Graduate School, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul, 34056, South Korea

    Anh Duc Pham

  3. Department of Mechanical Engineering, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul, 34056, South Korea

    Hyeong-Joon Ahn

Authors
  1. The Linh Tran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anh Duc Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyeong-Joon Ahn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hyeong-Joon Ahn.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tran, T.L., Pham, A.D. & Ahn, HJ. Lost motion analysis of one stage cycloid reducer considering tolerances. Int. J. Precis. Eng. Manuf. 17, 1009–1016 (2016). https://doi.org/10.1007/s12541-016-0123-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-016-0123-8

Keywords

Search

Navigation