Center of mass work analysis predicts preferred walking speeds for varying walking conditions

This study investigates the role of optimal push-off impulses in minimizing the total mechanical work dissipation per step, aiming to achieve passive single support work performance for a variety of walking conditions. By optimizing push-offs to cover the entire step's energy demands, the single support work may become only storage and release of mechanical energy through tendons and tissues when the soft tissue dissipation is negligible. Our simulations indicate that for each walking speed, there is an optimal push-off impulse that ensures energy balance without the need for additional energy regulation post step transition. The analytical optimal push-off coincided with minimum total step dissipation. The experimentally derived center of mass (COM) work components indicated that net single support work played a role in regulating COM momentum. For each walking condition examined, we identified only one specific walking speed at which the net single support work was zero. This speed also coincided with the minimum total step dissipation (the sum of step collision and net negative single support work). It was 64.2 % of the total step work for young adults walking on smooth surfaces. We defined the minimum total step dissipation as the indicator for mechanically preferred walking speed. For level ground (even terrain), the estimated mechanically preferred walking speeds align closely with literature values for young adult (age: 27.7 ± 5.2, speed: ∼1.2 m.s^-1) and older adult (age: 66.1 ± 1.4, speed: ∼ 1.0 m.s^-1) self-selected speeds, with a reduction observed for the restricted view of oncoming irregularities in the substrate terrain (15 %). For walking on uneven surfaces, terrain amplitude was shown to impact walking costs quadratically, with optimal speeds declining by approximately 20 % per unit increase in terrain amplitude. We also observed that the preferred speeds for older adults tend to be 12-15 % lower than for younger adults, likely due to biomechanical adaptations. Beyond certain terrain amplitudes, no preferred walking speed allowed fully passive single support work, highlighting a possible biomechanical threshold where ankle push-off alone becomes insufficient and hip torque compensation may be necessary. This approach provides a framework for estimating mechanically preferred walking speeds across varying walking conditions such as different terrain amplitudes when the total step dissipation is minimized.