Estimation of Torque Variation from Pedal Motion in Cycling

Abstract

In cycling, the pedalling technique is determined mostly by variations in the torque applied to the pedals during crank rotation. We developed and validated a method to compute these variations from the pedalling motion using an ergometer. The torque at the pedal is the sum of the torques needed to overcome all resistive forces and the torque required for any changes of angular momentum of the ergometer flywheel. This last torque is proportional to the angular acceleration of the crank. For an ergometer with almost constant brake torque, we may assume that variations in the pedal force can be extracted from the pedal motion alone. The key problem is to reliably estimate the angular pedal acceleration from noisy 3D motion capture (MoCap) or 2D video data. We projected the positional data onto a least squares fitting circle, then filtered the resulting angular time sequence by local polynomial regression. Finally, we solved the torque equilibrium equation for the pedal torque. For validation of the method, we used direct pedal torque measurement. In our experiments, pedal brake forces ranged between 100 and 250 N, and cadences of 60, 80, and 100 rpm were used. The pedal torque results from MoCap were better than from video. The results from video were close to MoCap results when a correction of the marker position was applied.