Although joint angle is commonly computed from the coordinates of the joint centers as a user-angle (see the User-Angle Issues section for the details), it can be also computed from the relative orientation angles of the joint. In 1-DOF joints such as the hinge joint, the joint angle corresponds to one of the orientation angles and no additional computation is required. But in joints with more than 1 DOF, additional computation must be performed to obtain the joint angle.
From  of Computation of the Orientation Angles:
where TD/P = the transformation matrix from the proximal reference frame to the distal reference frame at a joint, and = the relative orientation angles between the segments at the joint. Now, let's assume that the Z axes of the segmental reference frames coincide with their respective longitudinal axes of the segments:
where s = the unit vector of a segment's longitudinal axis.
As one can see in , the longitudinal axis vector of the distal segment described in the proximal reference frame has nothing to do with angle because it is the rotation angle about the Z axis. The angle between the longitudinal axes of the proximal and distal segments forming a joint () can be computed from the scalar product of the two s vectors: from  and ,
Thus, the joint angle is
© Young-Hoo Kwon, 1998-