A new technique for determining 3-D joint angles: The tilt/twist method
Objective. To develop a new method of representing 3-D joint angles that is both physically meaningful and mathematically stable. Design The two halves of a joint are modeled as overlapping cylinders. This simple physical model is easily understood and yields mathematically stable angle equations. Background. Two currently-used methods are the Euler/Cardan (joint coordinate system) method and the projection angle method. Both of these methods approach a singularity at 90°that limits their use. The helical angle (attitude vector) method is mathematically stable but has limited physical meaning and is difficult to communicate. Methods. Calculation of the tilt/twist angles is described. Tilt/twist angles are compared to Euler/Cardan, projection, and helical angles in terms of behavior and stability. Results. Through a small range of angulation, tilt/twist angles match the specific projection and Euler/Cardan angles previously studied. Although not as stable as helical angles, tilt/twist angles are twice as stable as Euler/Cardan and projection angles, reaching a singularity only at 180°. Conclusions. Because of their mathematical stability and simple physical interpretation, tilt/twist angles are recommended as a standard in describing angular joint motion.
Digital Object Identifier (DOI)
Crawford, Neil R.; Yamaguchi, Gary T.; and Dickman, Curtis A., "A new technique for determining 3-D joint angles: The tilt/twist method" (1999). Neurobiology. 859.