Fig 1.
Definition of the ISA with respect to the world coordinate system.
Fig 2.
Definition of the ASA calculated as the average orientation of the ISAs and the optimal pseudo-intersection of the ISAs.
Fig 3.
Analysis of the dispersion of the ISAs with respect to the ASA, represented as the confidence ellipsoid.
Fig 4.
Poses of femur and tibia across one gait cycle.
The motion progresses from the left to the right. CS0 is the world coordinate system, CS1 is the coordinate system attached to the femur, CS2 is the coordinate system attached to the tibia. For CS 1 and CS 2, the x-axis is pointing forward, the y-axis is pointing upwards while the z-axis is on the medio-lateral direction.
Fig 5.
a) Experimental setup for the hinge measurements and b) the three-dimensional reconstruction of the motion of the artificial hinge. The poses of the two segments are visualized.
Fig 6.
Generated data for a swing cycle about an ideal cylindrical joint.
Table 1.
Effect of the regularization: Common normal distance and position point (SASA) of the regularized ASA with respect to the non-regularized ASA.
Fig 7.
Sensitivity analysis, as calculated for ϵ = 0.01.
Standard deviation (SD) of (a) the angle between the ASA with noise and without noise; (b) the common-normal distance between the two axes; (c) the SASA distance.
Fig 8.
Ellipsoid of the dispersion analysis in the case of: (a) gait; (b) hinge; (c) ideal hinge, each time represented in the CS attached to the ASA. In the last case, the ellipsoid degenerated to the ASA axis itself.
Table 2.
Results of the dispersion analysis.