Model and analysis of pedals ergonomic load torque angular distribution in the pedaling-by-wire system

A novel, homogeneous and continuous analytical model of cyclist pedaling torque angular distribution is presented in the article. The model is dedicated for use in an unique pedaling-by-wire system. The motivation to the research is to obtain a model for use in control system with compensation. Applying nonlinear compensation of cyclist load torque results in pedals speed ripples reduction - particularly noticeable at high torque loads. Theoretical assumptions to the model are described in the article with use of kinematics relations marked both on vehicle photography and detailed sketches. Inverse kinematics formulas are verified by comparison two different methods of formulating the kinematic equations of the model. Those methods bases on geometric and vector approach are different in computation complexity. The model of dynamics is presented with its physical fundamentals explanation. Adaptation system of presented model parameters is introduced basing on the Gauss-Newton algorithm. Fitting process is described on the example of three experimental reference data acquired at three different torque loads. Final results of parameters adaptation are presented in the graphical and numerical way by using chi2 coefficient. Further research plans based on obtained results are included in the article summary section.