A Closed-Form Solution for Human Finger Positioning

Abstract

In this paper we describe a novel technique for solving the inverse kinematics problem for human fingers. We derive a closed-form solution that places the fingertips precisely in the desired location by allowing minor deviations in the rotations of the Proximal Interphalangeal and Distal Interphalangeal joints compared to the fixed ratio that is known to exist between them. The obvious advantage is that with our approach there is no need to iterate until the distance between the fingertips and the desired locations is small enough. We show that this method is reliable and exact while showing minimal differences to the finger poses generated by the original closed-form solution. In our experiments we found the positions of the intermediate joints of the finger to deviate only around 1.5 mm in the worst case from those resulting from a numerical approximation of the original closed-form solution. On average the deviation is less than 0.5 millimeter.