The relationship between smoothness and economy during walking

The purpose of this study was to test a theoretical model (Stein et al. 1986) which suggested that minimizing the rate of metabolic energy consumption (\(\dot V\)O₂) is related to minimizing jerk (third derivative of position) during human movement. At a given speed of walking, \(\dot V\)O₂ has been shown to increase curvilinearly as stride length (SL) is varied from freely chosen stride length (FCSL). It was hypothesized that the jerk-cost, or JC (area under squared jerk curve), would exhibit similar behavior. Subjects (n=24) walked (1.75 m ·. s⁻¹) on a treadmill at FCSL, and at SL derivations at ± 10 and ±20% of leg length from FCSL until steady-state \(\dot V\)O₂ was attained. Videotaping (60 Hz) in the sagittal plane and subsequent digitizing of relevant markers produced position coordinates which were smoothed and normalized in both distance and time before calculating the third time derivative to obtain two-dimensional JC values. The expected response of \(\dot V\)O₂ to deviations in SL was found (minimum at FCSL), but JC increased with SL except at the two longest SL conditions. A weak but statistically significant negative correlation was found between \(\dot V\)O₂ and JC, suggesting that smoothness and economy are not complementary performance criteria during walking.