A state-space analysis of mechanical energy generation, absorption, and transfer during pedaling

Abstract

Seated ergometer pedaling is a motor task ideal for studying basic mechanisms of human bipedal coordination because, in contrast to standing and walking, fewer degrees of freedom are being controlled and upright balance is not a factor. As a step toward understanding how individual muscles coordinate pedaling, we investigated how individual net muscle joint torques and non-muscular (e.g. centripetal, coriolis, and gravity) forces of the lower limbs generate, absorb, and transfer mechanical energy in order to propel the crank and recover the limb. This was accomplished using a mechanical power analysis derived entirely from the closed-form state-space dynamical equations of a two-legged pedaling model that accounted for both the limb segmental and crank load dynamics. Based on a pedaling simulation that reproduced experimental kinematic and kinetic trajectories, we found that the net ankle and hip extensor joint torques function ‘synergistically’ to deliver energy to the crank during the downstroke. The net hip extensor joint torque generates energy to the limb, while the net ankle extensor joint torque transfers this energy from the limb to the crank. In contrast, net knee extensor and flexor joint torques function ‘independently’ by generating energy to the crank through the top and bottom of the stroke, respectively. The net ankle joint torque transfers and the net knee joint torque generates energy to the crank by contributing to the driving component of the pedal reaction force. During the upstroke, net ankle extensor joint torque transfers energy from the crank to the limb to restore the potential energy of the limb. In both halves of the crank cycle, gravity forces augment the crank-limb energy transfer performed by the net ankle extensor joint torque.