Modelling of the toe trajectory during normal gait using circle-fit approximation

This work aimed to validate the approach of using a circle to fit the toe trajectory relative to the hip and to investigate linear regression models for describing such toe trajectories from normal gait. Twenty-four subjects walked at seven speeds. Best-fit circle algorithms were developed to approximate the relative toe trajectory using a circle. It was detected that the mean approximation error between the toe trajectory and its best-fit circle was less than 4 %. Regarding the best-fit circles for the toe trajectories from all subjects, the normalised radius was constant, while the normalised centre offset reduced when the walking cadence increased; the curve range generally had a positive linear relationship with the walking cadence. The regression functions of the circle radius, the centre offset and the curve range with leg length and walking cadence were definitively defined. This study demonstrated that circle-fit approximation of the relative toe trajectories is generally applicable in normal gait. The functions provided a quantitative description of the relative toe trajectories. These results have potential application for design of gait rehabilitation technologies.