Skip to main content
Log in

Generation method of asymmetric chainring design from pedaling torque experimental data

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In cycling, pedaling is a bilateral asymmetries function that related to leg dominance. However, studies about the asymmetric shape on the chainring design considering pedaling asymmetries function and the test are limited. In this paper, a method to generate an asymmetric chainring from the experimental data is proposed. The curve fitting method and the flowchart to synthesize the asymmetric shape from the crank torque data are presented. The experimental test to compare the chainring prototype and the circular chainring on the same number of teeth is conducted. The comparison test is performed by comparing the downstroke torque and power at the same rotational speed on the rear wheel. The result indicates that pedaling on the asymmetric chainring prototype is more efficient and lighter than circular chainring. This work can be used as a guidance procedure to design any asymmetric chainring from the experimental data.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Abbreviations

N :

Number of teeth

S :

Total arch length

p :

Chain pitch

dt :

Net torque data

mv :

Multiplier value

L n :

Distance between two points in segment “n”

S n :

Slope on point “n”

f n (x) :

Shape equation of segment “n”

a 0, a 1, a 2, a 3 :

Unknown parameters in the shape equation

References

  1. G. Li and W. Zhu, Design and power loss evaluation of a non-circular gear pair for an infinitely variable transmission, Mechanism and Machine Theory, 156 (2021) 1–17.

    Article  Google Scholar 

  2. X. F. Wang and W. D. Zhu, Dynamic analysis of an automotive belt-drive system with a noncircular sprocket by a modified incremental harmonic balance method, Journal of Vibration and Acoustics, 139(1) (2017) 1–13.

    Article  Google Scholar 

  3. D. B. Dooner, Function generation utilizing an eight-link mechanism and optimized non-circular gear elements with application to automotive steering, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 215(7) (2001) 847–857.

    Google Scholar 

  4. C. Lin, Y. Hu, Y. Wei and Z. Cai, Characteristics analysis of supporting and locking mechanism based on the non-circular gear compound transmission, Journal of Mechanical Science and Technology, 34(6) (2020) 2561–2571.

    Article  Google Scholar 

  5. D. Liu, Y. Ba and T. Ren, Flow fluctuation abatement of high-order elliptical gear pump by external noncircular gear drive, Mechanism and Machine Theory, 134 (2019) 338–348.

    Article  Google Scholar 

  6. B. W. Bair, M. H. Sung, J. S. Wang and C. F. Chen, Tooth profile generation and analysis of oval gears with circular-arc teeth, Mechanism and Machine Theory, 44(6) (2009) 1306–1317.

    Article  MATH  Google Scholar 

  7. S. Park, J. Bae, Y. Jeon, K. Chu, J. Bak, T. W. Seo and J. Kim, Optimal design of toggle-linkage mechanism for clamping applications, Mechanism and Machine Theory, 120 (2018) 203–212.

    Article  Google Scholar 

  8. E. Zheng, F. Jia, H. Sha and S. Wang, Non-circular belt transmission design of mechanical press, Mechanism and Machine Theory, 57 (2012) 126–138.

    Article  Google Scholar 

  9. J. Ye, X. Zhao, Y. Wang, X. C. Sun, J. N. Chen and X. D. Xia, A novel planar motion generation method based on the synthesis of planetary gear train with noncircular gears, Journal of Mechanical Science and Technology, 33(10) (2019) 4939–4949.

    Article  Google Scholar 

  10. D. B. Dooner, Use of noncircular gears to reduce torque and speed fluctuations in rotating shafts, Journal of Mechanical Design, 119(2) (1997) 299–306.

    Article  Google Scholar 

  11. Y. A. Yao and H. S. Yan, A new method for torque balancing of planar linkages using non-circular gears, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 217(5) (2003) 495–503.

    Google Scholar 

  12. I. S. Kochev, Full shaking moment balancing of planar linkages by a prescribed input speed fluctuation, Mechanism and Machine Theory, 25(4) (1990) 459–466.

    Article  Google Scholar 

  13. D. Mundo, Geometric design of a planetary gear train with non-circular gears, Mechanism and Machine Theory, 41(4) (2006) 456–472.

    Article  MATH  Google Scholar 

  14. S. Okajima, Designing chainwheels to optimize the human engine, Bike Tech, 2(4) (1983) 1–7.

    Google Scholar 

  15. N. R. Miller and D. Ross, The design of variable-ratio chain drives for bicycles and ergometers — application to a maximum power bicycle drive, Journal of Mechanical Design, 102(4) (1980) 711–717.

    Article  Google Scholar 

  16. F. Freudenstein and C. K. Chen, Variable-ratio chain drives with noncircular sprockets and minimum slack-theory and application, Journal of Mechanical Design, 113(3) (1991) 253–262.

    Article  Google Scholar 

  17. R. P. S. Han, M. A. Thomlinson and Y. S. Tu, Kinematics and kinetics of a non-circular bicycle drive system, Mechanism and Machine Theory, 26(4) (1991) 375–388.

    Article  Google Scholar 

  18. R. P. S. Han and K. Alexander, An optimum non-circular chainwheel design for a bicycle drive system, Journal of the Franklin Institute, 330(6) (1993) 1195–1217.

    Article  Google Scholar 

  19. L. K. Cullen, K. Andrew, K. R. Lair, M. J. Widger and B. F. Timson, Efficiency of trained cyclists using circular and noncircular chainrings, International Journal of Sports Medicine, 13(3) (1992) 264–269.

    Article  Google Scholar 

  20. M. L. Hull, M. Williams, K. Williams and S. Kautz, Physiological response to cycling with both circular and noncircular chainrings, Medicine and Science in Sports and Exercise, 24(10) (1992) 1114–1122.

    Article  Google Scholar 

  21. E. A. Hansen, K. Jensen, J. Hallén, J. Rasmussen and P. K. Pedersen, Effect of chain wheel shape on crank torque, freely chosen pedal rate, and physiological responses during sub-maximal cycling, Journal of Physiological Anthropology, 28(6) (2009) 261–267.

    Article  Google Scholar 

  22. F. P. Carpes, F. Dagnese, C. B. Mota and D. J. Stefanyshyn, Cycling with noncircular chainring system changes the three-dimensional kinematics of the lower limbs, Sports Biomechanics, 8(4) (2009) 275–283.

    Article  Google Scholar 

  23. J. Peiffer and C. Abbiss, The influence of elliptical chainrings on 10 km cycling time trial performance, International Journal of Sports Physiology and Performance, 5(4) (2010) 459–468.

    Article  Google Scholar 

  24. F. Dagnese, F. P. Carpes, E. A. Martins, D. Stefanyshyn and C. B. Mota, Effects of a noncircular chainring system on muscle activation during cycling, Journal of Electromyography and Kinesiology, 21(1) (2011) 13–17.

    Article  Google Scholar 

  25. M. Mateo-March, M. Zabala and J. J. González-Badillo, Effects of the orientation of the maximum torque point with a Q-Ring non-circular chainring system on the BMX cycling sprint performance, Science and Sports, 27(3) (2012) e15–e19.

    Article  Google Scholar 

  26. A. Cordova, I. Latasa, J. Seco, G. Villa and J. Rodriguez-Falces, Physiological responses during cycling with oval chainrings (Q-ring) and circular chainrings, Journal of Sports Science and Medicine, 13(2) (2014) 410–416.

    Google Scholar 

  27. M. Mateo-March, E. Fernández-Peña, C. Blasco-Lafarga, J. Morente-Sánchez and M. Zabala, Does a non-circular chainring improve performance in the bicycle motocross cycling start sprint?, Journal of Sports Science and Medicine, 13(1) (2014) 97–104.

    Google Scholar 

  28. G. Strutzenberger, T. Wunsch, J. Kroell, J. Dastl and H. Schwameder, Effect of chainring ovality on joint power during cycling at different workloads and cadences, Sports Biomechanics, 13(2) (2014) 97–108.

    Article  Google Scholar 

  29. C. H. Leong, S. J. Elmer and J. C. Martin, Noncircular chainrings do not influence maximum cycling power, Journal of Applied Biomechanics, 33(6) (2017) 410–418.

    Article  Google Scholar 

  30. N. Horvais, P. Samozino, K. Zameziati, C. Hautier and F. Hintzy, Effects of a non circular chainring on muscular, mechanical and physiological parameters during cycle ergometer tests, Isokinetics and Exercise Science, 15(4) (2007) 271–279.

    Article  Google Scholar 

  31. F. Hintzy and N. Horvais, Non-circular chainring improves aerobic cycling performance in non-cyclists, European Journal of Sport Science, 16(4) (2016) 427–432.

    Article  Google Scholar 

  32. A. E. Jeukendrup and J. Martin, Improving cycling performance, Sports Medicine, 31(7) (2001) 559–569.

    Article  Google Scholar 

  33. R. R. Bini and P. A. Hume, Assessment of bilateral asymmetry in cycling using a commercial instrumented crank system and instrumented pedals, International Journal of Sports Physiology and Performance, 9(5) (2014) 876–881.

    Article  Google Scholar 

  34. I. Rannama and K. Port, Bilateral biomechanical asymmetry during 30 seconds isokinetic sprint-cycling exercise, LASE Journal of Sport Science, 6(2) (2015) 3–16.

    Google Scholar 

  35. F. P. Carpes, M. Rossato, I. E. Faria and C. B. Mota, Bilateral pedaling asymmetry during a simulated 40-km cycling time-trial, The Journal of Sports Medicine and Physical Fitness, 47(1) (2007) 51–57.

    Google Scholar 

  36. F. P. Carpes, M. Rossato, I. E. Faria and C. B. Mota, During an incremental exercise cyclists improve bilateral pedaling symmetry, Brazilian Journal of Biomotricity, 2(3) (2008) 155–159.

    Google Scholar 

  37. A. H. Fowler and C. W. Wilson, Cubic Spline: A Curve Fitting Routine, Union Carbide Corp, Oak Ridge, USA (1966).

    Book  Google Scholar 

  38. S. L. Chang, C. P. Jiang, F. Y. Tasi, X. B. Hong, C. C. Chi and C. W. Shao, CAD/CAM of the sprocket and the efficiency test, Advanced Materials Research, 295 (2011) 2406–2412.

    Article  Google Scholar 

  39. JIS B 1801:1997, Short-Pitch Transmission Precision Roller Chains and Bush Chains, Japanese Standards Association, Japan (1997).

    Google Scholar 

Download references

Acknowledgments

This work was supported by the Ministry of Science and Technology of the ROC [grant number MOST 109-2221-E-150-011]. Prototyping was supported by SAMOX Company.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shinn-Liang Chang.

Additional information

Ardi Lesmawanto is a Ph.D. candidate in Department of Power Mechanical Engineering, National Formosa University, Taiwan. He also a lecturer in Mechanical Engineering Department, University of Muhammadiyah Malang, Indonesia. His research interests include noncircular sprocket design, and grinding wheel applications in cutting tools.

Kao-Kuei Hsu is a lecturer and instructor in Office of Physical Education, National Formosa University, Taiwan. His research interests include basketball, swimming, sport injuries, and exercise physiology.

Shinn-Liang Chang is a Professor in Department of Power Mechanical Engineering, National Formosa University, Taiwan. He received his Ph.D. from National Chiao Tung University. His research interests include mechanism, gear principle and application, cutting tool design and manufacturing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lesmawanto, A., Hsu, KK. & Chang, SL. Generation method of asymmetric chainring design from pedaling torque experimental data. J Mech Sci Technol 36, 6115–6122 (2022). https://doi.org/10.1007/s12206-022-1126-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-022-1126-2

Keywords

Navigation