Rigid Body Motion Calculated From Spatial Co-ordinates of Markers

Abstract

In this paper, we present a unified method for calculating spatial coordinates of markers for a rigid body motion such as in bones. Kinematical analysis of bone movement in cadaveric specimens or living objects had been developed. Here, we show how spatial co-ordinates of markers in or on bone can be calculated from the co-ordinates of projections of these markers in two different directions on one or two planes. This rigid body motion can be described by a rotation matrix and a translation vector or by the position of screw axis, the angle of rotation about this axis and the translation along the axis. Our method shows that our solution process is different and our results show that three or more non-collinear points are used and no initial approximation is needed.