title: A new technique for determining 3-D joint angles: the tilt/twist method.
abstract: OBJECTIVE
  To develop a new method of representing 3-D joint angles that is both physically meaningful and mathematically stable.
  
  
  METHODS
  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.
authors.affiliation: Spinal Biomechanics Research Laboratory, Barrow Neurological Institute, Phoenix, AZ 85013, USA. ncrawfo@chw.edu
authors.forename: N R
authors.initials: NR
authors.lastname: Crawford
authors.forename: G T
authors.initials: GT
authors.lastname: Yamaguchi
authors.forename: C A
authors.initials: CA
authors.lastname: Dickman
mesh_terms: D001696:Biomechanical Phenomena; D006801:Humans; D007593:Joint Instability / Q000503:physiopathology; D008953:Models, Anatomic; D008954:Models, Biological; D016059:Range of Motion, Articular / Q000502:physiology*; D012680:Sensitivity and Specificity; D013131:Spine / Q000033:anatomy & histology / Q000502:physiology*