Figure 1. Experimental vs. standard helical axis parameters. (A) Diagram of the experimental and standard helical parameters. Experimental helical axis parameters are calculated from the digital image of the mandible at two locations, A and B, defined by the centric and eccentric interocclusal record images (Spoor and Veldpaus, 1980). The unit vector E defines the orientation of the helical axis. The angle between the experimental and standard helical axis unit vectors, E, was calculated with the use of a second unit vector, É_Exp that points in the same direction as E_Exp and originates from P_Std. The vector P, which points from the origin to a point on a line defined by E, defines the position of the helical axis. Differences in the experimental and standard position vectors, P, were calculated indirectly as the minimum distance, d, between the two lines defined by the helical axes (Zwillinger, 1996), because the 3D distance between P_Exp and P_Std is not necessarily the minimum distance between the lines. Equations for the difference calculations are shown in (A). Mean differences between experimental and standard helical axis parameters are shown in (B) through (E) as a function of jaw movement expressed as a rotation about the helical axis (n = 5; error bars representing the standard deviations are smaller than the data symbols). Qualitatively, the angle (B) and the distance (C) between the experimental and standard helical axes are similar to the helical axis error model predictions represented by the "best fit" dashed line (Spoor, 1984; Woltring et al., 1985; de Lange et al., 1990b). The differences between the experimental and standard rotations about the helical axis (D) and translations along the helical axis (E) are nearly constant, as predicted by the helical axis error model, and are smaller than the 0.040 mm accuracy of the Comet 100 scanner.

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