Multivariable optimization of cycling biomechanics.

Relying on a biomechanical model of the lower limb which treats the leg-bicycle system as a five-bar linkage constrained to plane motion, a cost function derived from the joint moments developed during cycling is computed. At constant average power of 200 W, the effect of five variables on the cost function is studied. The five variables are pedalling rate, crank arm length, seat tube angle, seat height, and longitudinal foot position on the pedal. A sensitivity analysis of each of the five variables shows that pedalling rate is the most sensitive, followed by the crank arm length, seat tube angle, seat height, and longitudinal foot position on the pedal (the least sensitive). Based on Powell's method, a multivariable optimization search is made for the combination of variable values which minimize the cost function. For a rider of average anthropometry (height 1.78 m, weight 72.5 kg), a pedalling rate of 115 rev min-1, crank arm length of 0.140 m, seat tube angle of 76 degrees, seat height plus crank arm length equal to 97% of trochanteric leg length, and longitudinal foot position on the pedal equal to 54% of foot length correspond to the cost function global minimum. The effect of anthropometric parameter variations is also examined and these variations influence the results significantly. The optimal crank arm length, seat height, and longitudinal foot position on the pedal increase as the size of rider increases whereas the optimal cadence and seat tube angle decrease as the rider's size increases. The dependence of optimization results on anthropometric parameters emphasizes the importance of tailoring bicycle equipment to the anthropometry of the individual.