Instantaneous Helical Axis Estimation Via Natural, Cross-Validated Splines

Abstract

In studies of biological joint motion, quantification of translations and rotations by means of a reference point and attitude angles does not provide a clear insight in the relation between kinematics and joint geometry. Because of its geometric simplicity, a better picture can be obtained by means of the Instantaneous Helical Axis (IHA), also known as the instantaneous screw axis, twist axis, or axis of rotation. At each moment in time, joint motion is seen as the movement of one body segment with respect to an adjacent segment (usually distal with respect to proximal), with a translation component along, and a rotation component about a directed line in space which is uniquely determined as long as the rotatory component does not vanish: see Figure 1. The total amounts of translation and rotation along the path of motion can be defined as the time integrals of the instantaneous translation and rotation velocities at the IHA from a given reference time.