Modelling error distribution in the ground reaction force during an induced-acceleration analysis of running in rear-foot strikers

The objective of this study was to develop and evaluate a methodology for quantifying the contributions of modelling error terms, as well as individual joint torque, gravitational force and motion-dependent terms, to the generation of ground reaction force (GRF), whose true value can be measured with high accuracy using a force platform. Dynamic contributions to the GRF were derived from the combination of 1) the equations of motion for the individual segments, 2) the equations for constraint conditions arising from the connection of adjacent segments at joints, and 3) the equations for anatomical constraint axes at certain joints. The contribution of the error term was divided into four components caused by fluctuation of segment lengths, geometric variation in the constraint joint axes, and residual joint force and moment errors. The proposed methodology was applied to the running motion of thirteen rear-foot strikers at a constant speed of 3.3 m/s. Modelling errors arose primarily from fluctuations in support leg segment lengths and rapid movement of the virtual joint between the foot and ground during the first 20% of stance phase. The magnitudes of these error contributions to the vertical and anterior/posterior components of the GRF are presented alongside the non-error contributions, of which the joint torque term was the largest