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

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

Journal Article


​​​​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 requires 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% more accurate while at the highest
noise levels the ECR method is up to 100% more accurate. The ECR
results over the entire range of noise levels reveals an average
improvement on the order 20% 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.


Trans. ASME, Journal of Biomechanical Engineering, Vol 122, No 4, pp 437-445
01 Jan 2000
B. Dariush, H. Hemami, M. Parnianpour