Non-circular chainrings for cycling

1. Why do appropriate non-circular chainrings yield more crank power compared to conventional circular systems during isokinetic pedaling?

Copyright © 2012, by the authors:

L. Malfait, M.Mech.Eng.
G. Storme, M.Sc.Mech.Eng.
M. Derdeyn, M.Sc.Mech.Eng & Appl.Math.

Abstract – Several studies have been published on the use of eccentric and non-circular chainrings.The findings of these studies have, however, not been consistent. Despite the lack of consistent positive results in terms of physiological responses, a consensus appears to prevail that the improved mechanical effectiveness of the oval chainring may lead to performance enhancement (e.g. increased crank power output) compared to the conventional circular chainwheel. Some authors assume non-circular chainrings may improve pedal dynamics by reducing the effect of the "dead spot" in the pedaling cycle. Other argue that an elliptical chainwheel should more efficiently match the torque output capability of the rider to the torque input requirement of the pedaling cycle. Still other researchers conclude that non-circular chainrings can potentially increase crank power relative to a conventional circular chainring by acting to slowdown the crank angular velocity during the downstroke (power phase) which allows muscles to generate power longer and to produce more external work. The pedal reaction force can be decomposed into a limb-static force and a limb-dynamic force (gravity and inertial effects) component. Static forces result from pedal forces only. Dynamic forces and dynamic moments are needed to accelerate/decelerate (to move) the lower limbs. As a consequence crank power, joint-moments and joint-power are the result of static pedal forces and of the dynamic forces/moments. In a theoretical model, by assuming the static pedal forces being zero it becomes possible to investigate the specific impact of the change of the dynamic force component on the bicycle-rider system. Altering the dynamic forces/moments is possible via ovality and shape of the chainring, crank orientation angle, pedaling cadence, anthropometric values and bike geometry. The objective of this study was, relying on a torque-driven bicycle-rider musculoskeletal model, first, to study the dynamic joint-moments and dynamic joint-power as a function of ovality and shape of the chainring, crank orientation angle and pedaling cadence during isokinetic pedaling. Second, to study the dynamic crank power output of non-circular chainrings when applying the instantaneous dynamic joint-moments of the circular chainwheel on the non-circular chainring. In this case, per definition, the instantaneous dynamic crank power and average dynamic crank power equal zero for the circular chainring. But the dynamic average crank power of the non-circular chainring, when applying the dynamic joint-loads of the circular chainring, will result in either an average crank power gain or an average crank power loss compared to circular. For each of the examined non-circular chainrings, the impact of crank orientation angle and pedaling cadences are investigated. As a general conclusion, the results of the study indicate that optimizing the dynamic component of the joint-load by designing an appropriate non-circular chainring (ovality, shape, crank orientation angle and cadence):
- gives rise to favourable differences in curve profiles and peak-values for both the dynamic joint-moments and dynamic joint-powers compared to circular
- leads to a measurable crank power gain when applying the dynamic joint-moments of the circular on the appropriate non-circular chainwheel. This means that the dynamic joint-moments/forces needed to accelerate/decelerate the limbs with a circular chainwheel are delivering the dynamic joint-power needed to move the lower limbs with the appropriate non-circular chainring and are yielding a crank power surplus.

Link to the integral text of the study: Appropriate non-circular chainrings.pdf (file size: appr. 2.73 MB)

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2. Comparative biomechanical study of circular and non-circular chainrings for endurance cycling at constant speed. Release 2.

Copyright © 2006 (release 1) – 2010 (release 2), by the authors:

L. Malfait, M.Mech.Eng.
G. Storme, M.Sc.Mech.Eng.
M. Derdeyn, M.Sc.Mech.Eng & Appl.Math.

Abstract – Non-circular chainrings have been available in cycling since the 1890’s. More recently, Shimano’s Biopace disaster has spoiled the market for oval chainrings. The Harmonic (1994) was re-launched in 2004 under the brand name O.symetric with some important successes in professional cycling. In 2005, the Q-Ring (Rotor) entered the cycling scene. However, non-circular chainwheels have not yet conquered the cycling world. There are many reasons for this: the conservative world of cycling, the suffocating market domination of an important manufacturer (and sponsor) of circular chainrings, the difficult bio-dynamics not understood by users and last but not least, it is not easy to measure and to prove the advantages of non-circular versus circular. Any reasonable non-circular chainwheel has about 50% chance of being better than the circular shape. The only question is: what is the optimum shape and how large can the difference be? The objective of this paper is to compare different chainring designs. Relying on a mathematical model a biomechanical comparison was made between circular and non-circular chainrings. The results of the study indicate clearly that (Criterion 1) for equal crank power for both circular and non-circular chainwheels, the peak joint power loads can be influenced favourably by using non-circular designs. For equal joint moments (Criterion 2) for both circular and non-circular designs, the model calculates differences in total crank power and differences in peak joint power loads. Results for both criteria are mostly concurrent. The analysis also indicates that shape as well as ovality, but also orientation of the crank relative to the chainring are important parameters for optimum design. It was found that some non-circular shapes are clearly better than other designs. The mathematical model can also be used as a tool for design optimization. Besides the commercial available non-circular chainrings, some ‘academic’ non-circular profiles were investigated.

Release 2 differs from the previous publication by the use of the MATLAB® software package for the mathematical (musculoskeletal) model in stead of programs developed in Pascal. Conclusions in release 2 completely confirm the findings from the first release, although with more moderate crank power efficiency gains. In release 2, the LM-S oval is added, result tables are replaced by graphs, a paragraph about optimal crank orientation is inserted and major parts of the text are reviewed or reworked.

Link to the integral text of the study: Biomechanical study chainrings - release 2.pdf (file size: appr. 1.45 MB)

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3. R&D projects/Scientific Tests & Studies:
  • Project 001: Comparative biomechanical study of Rotor System Crank

Comparative biomechanical study of a circular chainring and the Rotor System Crank (RSC) for endurance cycling at constant speed.
Biomechanical study - Rotor Crank System.pdf (file size: appr. 345KB)


  • Project 002: Effect of novel pedal design (Vista) on power output and joint loading.

By means of the biomechanical model the novel Vista Pedal was compared with a conventional pedal.
Biomechanical study - Vista Pedal.pdf (file size: appr. 99KB)


  • Project 003: Considerations about “Dead Centre” in cycling.

What is the exact meaning of the “Dead Centre” in the bicycle pedaling cycle?
Where is or are the “Dead Centre(s)” located?
Biomechanical study - Dead Centre.pdf (file size: appr. 66KB)


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Last update: 19th August 2017