A theoretical analysis of an optimal chainring shape to maximize crank power during isokinetic pedaling

Previous studies have sought to improve cycling performance by altering various aspects of the pedaling motion using novel crank–pedal mechanisms and non-circular chainrings. However, most designs have been based on empirical data and very few have provided significant improvements in cycling performance. The purpose of this study was to use a theoretical framework that included a detailed musculoskeletal model driven by individual muscle actuators, forward dynamic simulations and design optimization to determine if cycling performance (i.e., maximal power output) could be improved by optimizing the chainring shape to maximize average crank power during isokinetic pedaling conditions. The optimization identified a consistent non-circular chainring shape at pedaling rates of 60, 90 and 120 rpm with an average eccentricity of 1.29 that increased crank power by an average of 2.9% compared to a conventional circular chainring. The increase in average crank power was the result of the optimal chainrings slowing down the crank velocity during the downstroke (power phase) to allow muscles to generate power longer and produce more external work. The data also showed that chainrings with higher eccentricity increased negative muscle work following the power phase due to muscle activation–deactivation dynamics. Thus, the chainring shape that maximized average crank power balanced these competing demands by providing enough eccentricity to increase the external work generated by muscles during the power phase while minimizing negative work during the subsequent recovery phase.