Comparison of leg spring characteristics during running using mass-spring-damper modeling

• Main Author: Watanatada, Pasakorn
• Other Authors: Smith, Gerald A.
• Language: en_US
• Published: 2012
• Subjects: Running > Mathematical models; Leg > Mechanical properties > Mathematical models
• Online Access: http://hdl.handle.net/1957/32474

During heel-toe running, the vertical ground reaction force (VGRF) profile has both impact and active peaks. Although the mass-spring model (a single mass and a linear spring) is simple and useful to predict running characteristics, its simulation of VGRF profiles produces only a single peak rather than the double peak typically observed in running. In contrast, the mass-spring-damper model (two masses, two springs and a damper) produces a simulated force profile with two separate peak values. Running barefoot versus with shoes of varying stiffness produces VGRF profiles with quite different characteristics. The purpose of this study was to use the mass-spring and mass-spring-damper models to investigate the stiffness characteristics of human running in barefoot, hard-shoe and soft-shoe conditions. Ten recreational runners ran overground at 3.83 m/s and completed five trials of each footwear condition. Force data and two-dimensional kinematic data were recorded simultaneously at 1000 and 250 Hz respectively. Using the mass-spring model, vertical stiffnesses with the barefoot, hard-shoe and soft-shoe conditions were 27.6, 25.3 and 24.6 kN/m, respectively. Hard-shoe and soft-shoe material stiffnesses were about 150 and 100 kNm�����. Considering the leg and shoe as two springs in series, the leg's actual vertical stiffness could be estimated as 30 and 33 kNm����� for hard and soft-shoe conditions. The result suggested that runners increased their actual vertical stiffness with the sequence of barefoot, hard-shoe, and soft-shoe conditions. Using the mass-spring-damper model, the upper spring stiffness was relatively constant while the lower spring stiffness changed with footwear condition: 274, 136 and 126 kN/m, respectively. While it is mathematically convenient to model the leg and body with constant spring characteristics over time, physiologically it is likely that muscle-tendon stiffness does change during stance as muscle activity changes. This suggests that mass-spring models of running would be improved by time varying spring characteristics. Variable stiffness of the simple mass-spring model was tested using a smoothly varying stiffness function. This provided a significantly better force profile simulation for each of the footwear conditions than did the constant stiffness model. Further mass-spring-damper modeling may also be improved through incorporation of such time varying characteristics. === Graduation date: 2002