OPTIMIZATION TECHNIQUE FOR THE CALCULATION OF IN-VITRO 3-DIMENSIONAL VERTEBRAL MOTION

A method for the calculation of translations and Eulerian rotations of an orthogonal axis system with respect to a fixed reference is descri bed with application to the measurement of position in a vertebral mot ion segment. Kinematic equations were derived to compute the three-dim ensional motion of a moving vertebra relative to an adjacent fired bod y, without the requirement of a direct physical link between the two b odies. For this calculation, the quadratic error of the lengths of six position vectors was minimized to obtain a mathematically optimal est imate of the translations and rotations. Tests with a rigid model resu lted in mean maximum overall system errors of 2.8 percent for the meas urement of translation (translations less than 3.5 mm) and 6.1 percent for the measurement of rotations ( rotations less than 10 deg) limite d by transducer accuracy. The mathematical techniques presented for th e quantitative description of rigid body motion, based on the measurem ent of three reference vectors, may be extended to a broad range of ki nematic problems.