Definition of a Helical Angle for Three Dimensional Rotation.

Although the expression of three-dimensional rotation of the bone is very important for the diagnosis in orthopaedic surgery, there is no general definition of the angle. The mean rotation angle introduced by the author or Euler's angle makes the definition possible, but they depend on the local coordinate system introduced to the bone and they are not invariants independent of that coordinate system. On the other hand, the helical axis and rotation angle around it which are obtained through helical motion are invariants ; thus their introduction to the angular expression was proposed. The value of this angle, called helical angle, is compatible with that of the above mean rotation angle which has been used clinically due to its quasi-2-dimensional angular characteristics. Its effectiveness was investigated comparing the mean rotation angle and Euler's angle.