Classification of errors in locating a rigid body
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abstract
This paper discusses the manner in which random Gaussian errors affect the determination of body segment kinematics. For the process of modelling rigid body (RB) motion, three types of kinematic errors, input, measured and theoretical, are identified. These correspond to errors in: the determination of three-dimensional observed points, the RB fit of those points, and the estimation of true RB positions, respectively. Of these, the theoretical error is most critical and most pivotal. Accuracy is provided when the theoretical error is minimised, yet only the measured error can be minimised by RB modelling algorithms. In computer simulations one may determine the effect that such manipulations have on theoretical error, yet in most experimental conditions this value may not even be calculated. Fortunately, computer simulations can be performed to determine the inter-relationships between types of RB modelling errors. Such simulations can also be used to investigate the effects of RB shape. In this paper, Monte Carlo simulations were performed on three unit radius RBs; a triangle, a square and a tetrahedron. Although the use of the triangle provided the lowest measured error, this also coincided with the greatest theoretical error. The use of redundant points was found to yield superior theoretical accuracies. A slight advantage was gained with use of the non-planar point arrangement on the tetrahedron, both the measured and theoretical errors were reduced. Finally, the superiority of RB modelling over individual point tracking was reflected in all of the results; between 33 and 50% of the input error was eliminated with the use of RB modelling.
