Quantifying the human finger reachable space

Describing the flexibility of the hand using the reachable space concept has drawn the attention of many researchers in recent years. Existing approaches involving numerical techniques to obtain the reachable space are generally computationally expensive. In this study, we propose a resource-friendly approach to determine and quantify the bidimensional reachable space of the finger. The fundamental idea of the approach connects to a set of arc formulae for the boundary of the reachable space. These formulae of the boundary result a unique description to calculate the area of the reachable space using Green's theorem. Adopting this novel approach, reachable spaces can be visualised and quantified to effectively evaluate the functionality of different subjects and their therapeutic conditions. We evaluated the performance of the proposed approach against the popular kinematic feedforward approach and Monte Carlo simulation separately. The exclusive description of the reachable space boundary resulted in significant improvement to the execution time while delivering more accurate quantification values.