A correction for axis misalignment in the joint angle curves representing knee movement in gait analysis

This paper derives a simple mathematical model relating changes in the orientations of the two Cartesian coordinate systems involved in recording knee movement and the varus–valgus and the internal–external rotation angles for describing the knee's motion. Rotation matrices are given for changing the orientations of the two Cartesian coordinate systems in such a way that the quadratic variations in the varus–valgus and in the external–internal angles are minimal. These estimated rotation matrices are used to correct for axis misalignment. The correction is calibrated by considering the impact of the new orientation of the thigh Cartesian coordinate system on the hip joint angles. The procedure is applied to kinematic data collected on normal subjects. The uncertainty about the specification of the thigh Cartesian coordinate system is shown to explain some of the between subject variability in the varus–valgus and in the internal–external rotation angles curves.