A well-posed, embedded constraint representation of joint moments from kinesiological measurements

Joint moment estimation using the traditional inverse dynamics analysis presents two challenging problems, which limit its reliability. First, the quality of the computed moments depends directly on unreliable estimates of the segment accelerations obtained numerically by differentiating noisy marker measurements. Second, the representation of joint moments from combined video and force plate measurements belongs to a class of ill-posed problems, which does not possess a unique solution. This paper presents a well-posed representation derived from an embedded constraint equation. The proposed method, referred to as the embedded constraint representation (ECR), provides unique moment estimates, which satisfy all measurement constraints and boundary conditions and require fewer acceleration components than the traditional inverse dynamics method. Specifically, for an n-segment open chain planar system, the ECR requires n-3 acceleration components as compared to 3(n-1) components required by the traditional (from ground up) inverse dynamics analysis. Based on a simulated experiment using a simple three-segment model, the precision of the ECR is evaluated at different noise levels and compared to the traditional inverse dynamics technique. At the lowest noise levels, the inverse dynamics method is up to 50 percent more accurate while at the highest noise levels the ECR method is up to 100 percent more accurate. The ECR results over the entire range of noise levels reveals an average improvement on the order 20 percent in estimating the moments distal to the force plate and no significant improvement in estimating moments proximal to the force plate. The new method is particularly advantageous in a combined video, force plate, and accelerometery sensing strategy.