Geometric Design of Three-Phalanx Underactuated Fingers

This paper studies the grasp stability of two classes of three-phalanx underactuated fingers with transmission mechanisms based on either linkages or tendons and pulleys. The concept of underactuation in robotic fingers—with fewer actuators than degrees of freedom—allows the hand to adjust itself to an irregularly shaped object without complex control strategy and sensors. With a $n$-phalanx finger, $n$ contacts (one for each phalanx) are normally required to statically constrain the finger. However, some contact forces may be lacking due to either the transmission mechanism, or simply the object size and position. Thus, one may define an $ith$ order equilibrium, when the finger is in static equilibrium with $i$ missing contacts. In this paper, the case for which $n=3$ is studied with a particular emphasis on the cases for which $i=1$ and $i=2$⁠. The fact that some contact forces do not appear or are negative, can lead in some cases to the ejection of the object from the hand, when no equilibrium configuration is achieved.