The bicycle-rider system is modeled as a planar five-bar linkage with pedal forces and pedal dynamics as input. The pedal force profile input is varied, maintaining constant average bicycle power, in order to obtain the optimal pedal force profile that minimizes two cost functions. One cost function is based on joint moments and the other is based on muscle stresses. Predicted (optimal) pedal profiles as well as joint moment time histories are compared to representative real data to examine cost function appropriateness. Both cost functions offer reasonable predictions of pedal forces. The muscle stress cost function, however, better predicts joint moments. Predicted muscle activity also correlates well with myoelectric data. The factors that lead to effective (i.e. low cost) pedalling are examined. Pedalling effectiveness is found to be a complex function of pedal force vector orientation and muscle mechanics.