Letter to the Editor: Joint Moments in the Joint Coordinate System, Euler or Dual Euler Basis

Abstract

O'Reilly et al. [1] have efficiently introduced the dual Euler basis that is not always well understood in the biomechanical field. This brings new insights in the discussion on a preferred coordinate system for joint moments: inertial, proximal segment, distal segment or joint coordinate systems, but with two alternative bases (i.e., Euler and dual Euler) for the latter. It is noteworthy that in this longstanding discussion, the basic idea of using the JCS for joint moments was to express the joint angles and moments on the same anatomical axes (i.e., e1, e2, e3): “The intersegmental couple vector will then be presented in its scalar components which have functional significance. It is thought that the components along the joint coordinate systems defined above meet this requirement [6]. A joint moment M is a vector, and vectors should be decomposed into orthogonal components when doing calculations. We may choose the global coordinate system, or one of the segmental coordinate systems, to represent the components of M. However, when the calculations are finished, it might be good for presentation purposes to decompose M into nonorthogonal components, corresponding to the orientation of the JCS axes at that instant. This allows interpretation in terms of “flexion moment,â€‌ “adduction moment,â€‌ etc. [7]. We believe a more sensible approach is to express the forces and moments in terms of bodybased coordinate systems that have some anatomical significance. We have chosen the same axes used to define anatomical joint angles [8]. While it is important that complete 6DOF kinematic and forcemoment information be collected for a joint during testing, it is additionally critical that these quantities be described with respect to the same coordinate system [9]. We then favor the adoption of a joint coordinate system of axes; we also favor the use of the same joint system of axes for compatibility in reporting kinematic and kinetic data [10]. If a joint moment is thought to create a rotation about a joint and the JCS has been used to describe that rotation, then it would follow logically for the net moment vector to be expressed in the JCS as well [11]. Description of joint angles and joint moments in the same coordinate system may give a better biomechanical insight [12].â€‌