Tracking the articulated hand motion in a video sequence is a challenging problem in which the main difficulty arises from the complexity of searching for an optimal motion estimate in a high dimensional configuration space induced by the articulated motion. Considering that the complexities of this problem may be reduced by learning the lower dimensional manifold of the articulation motion in the configuration space, we propose a new representation for the non-linear manifold of the articulated motion, with a stochastic simplex algorithm that facilitates very efficient search. Contrary to traditional methods of representing the manifolds through clustering and transition matrix construction, we maintain the set of all training samples. To perform the search of best matching configuration with respect to the input image, we combine sequential Monte Carlo technique with the Nelder-Mead simplex search which is efficient and effective when the gradient is not readily accessible. This new approach has been successfully applied to hand tracking and our experiments show the efficiency and robustness of our algorithm.