A new technique for determining 3-D joint angles: the tilt/twist method

Clin Biomech (Bristol, Avon). 1999 Mar;14(3):153-65. doi: 10.1016/s0268-0033(98)00080-1.


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 degrees 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 found to be appropriate for describing spinal motion. Through larger ranges, tilt/twist angles do not match the other angles 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 degrees.

Conclusions: Because of their mathematical stability and simple physical interpretation, tilt/twist angles are recommended as a standard in describing angular joint motion.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Biomechanical Phenomena
  • Humans
  • Joint Instability / physiopathology
  • Models, Anatomic
  • Models, Biological*
  • Range of Motion, Articular / physiology*
  • Sensitivity and Specificity
  • Spine / anatomy & histology
  • Spine / physiology*