Abstract: Objective To obtain the three-dimensional (3D) motion space of ankle by an integral for the 3D rotation angle with mutual relationships of rotation angles in different directions, which is used to evaluate the flexibility and recovery of ankle more accurately and fully.Methods Twenty-five graduate students were recruited to participate in this study, one group consisted of 20 healthy individuals without ankle injury, and the other was composed of 5 patients with ankle injury. A motion capturing system was used to simultaneously capture the 3D coordinates of the marked points on the foot. Next, these 3D coordinates were converted into rotation angles through trigonometric functions processed. The maximum rotation angles of adduction, abduction, varus, and eversion change with the rotation angles of plantar flexion and dorsal flexure were measured by using polynomial fitting. At last, the size of the ankle's 3D motion space was obtained by integrating the fitting functions.Results The ankle's 3D motion space of the healthy people was 41.256, and the variation among them was less than 10%. The ankle's 3D motion space of the patient side was 33.163, and the variation among them was less than 15% because of the different degrees of rehabilitation. There was significant difference between two groups (t=8.804, P<0.01). With the same rotation angles of plantar flexion or dorsal flexure, the maximum rotation angle of varus was larger than that of eversion, and the maximum rotation angle of adduction was larger than that of abduction.Conclusion The algorithm can be used to quantify the 3D motion space of ankle more accurately, and to achieve a more comprehensive evaluation of ankle's flexibility and rehabilitation.

Key words: ankle, rehabilitative assessment, 3D motion space, polynomial fitting, integral, motion capture