Quantification of the finger functional range via explicit descriptions of reachable subspaces

In recent times, the finger flexibility assessment by means of reachable space is considered as an effective tool to describe the range of motion of the hand. Existing approaches numerically compute the reachable space using forward kinematics such as exhaustive scanning or Monte Carlo methods. In this paper, we provide explicit formulas mathematically determining the reachable space boundary. Green's theorem is used to deduce the corresponding capacity formula for the size of the reachable space as opposed to an implicit numerical solution. Using this new mechanism, we accurately quantify and compare the reachable space of different subjects in order to effectively compare the functionality of the fingers. We evaluate the performance of our proposed method against the kinematic feed-forward (KFF) approach in calculating the reachable space. The execution time to capture the reachable space is significantly less than that for the standard KFF method. The computational cost for quantifying the reachable space capacity is significantly improved due to explicit capacity formulas resulting from the abstract form of boundary descriptions of the reachable space, unique to the proposed approach.