The Fundamental Property of Human Leg During Walking: Linearity and Nonlinearity

Leg properties have been involved in the broad study of human walking from mechanical energy to motion prediction of robotics. However, the variable leg elasticities and their functions during gait have not been fully explored. This study presented that the fundamental leg properties during human walking comprise axial stiffness, rest leg length, tangential stiffness and force-free leg angles. We measured the axial force-leg length and tangential force-leg angle data in eight participants (mean ± s.d. age 24.6 ± 3.0 years, mass 68.2 ± 6.8 kg, height 177.5 ± 5.2 cm) at three self-selected walking speeds (slow: 1.25 ± 0.22, normal: 1.48 ± 0.28, fast: 1.75 ± 0.32 m/s) on two different contact conditions (fixed and moving). After obtaining these gait measurements, we extracted the linear and nonlinear leg elasticities during human walking by using a minimum root-mean-square fitting. We found that the axial stiffness of nonlinear elasticity (fixed condition: 7.1-8.0, moving condition: 21.3-22.6) is higher than that of the linear elasticity (fixed condition: 5.0-5.7, moving condition: 15.2-16.5). The tangential stiffness behaves different during four stance phases of gait, with the highest (linear: 2.52-3.72, nonlinear: 1.71-2.01, in moving condition) occurred at early stance and second highest at late stance, followed by two stiffnesses in mid-stance. For both linearity and nonlinearity, the axial stiffness and rest length are independent of walking speeds in both contact conditions, while the tangential stiffness and contact angles are independent of walking speeds only in moving condition. Regardless of walking speed, elasticity and contact condition, the force-free contact angle at mid-stance is maintained at average of 82.2 °. This paper first demonstrates the mechanical walking leg property from both axial and tangential aspects. The findings provide insight into the fundamental properties including linearity and nonlinearity of human leg during locomotion for stability analysis and precise motion prediction of robotics and rehabilitation exoskeletons.