Kinetostatic analysis of underactuated fingers

The aim of this paper is to establish a fundamental basis for the analysis of underactuated fingers with a general approach. A new method to obtain the force capabilities of any underactuated fingers will be presented. Force capability is defined as the ability to generate an external wrench onto a fixed object with a given set of phalanges. This method is based on the introduction of two new matrices which completely describe the relationship between the input torque of the finger actuator(s) and the contact forces on the phalanges. Using this tool, one can study the conditions under which certain phalanx forces vanish, and compare different underactuation mechanisms with a rigorous approach.

I. Introduction

Robotic hands have been developed with the aim of matching the human hand in terms of dexterity and adaptation capabilities to equip either a dextrous manipulator or a human being as a prosthetic device. Pioneer designs include: the Okada hand [1], the Stanford/JPL (Salisbury's) hand [2], the Utah/MIT hand [3], the Belgrade/USC hand [4], the BarrettHand [5], the hands from the DLR [6], [7], the LMS hand [8], or the NASA Robonaut hand [9]. However, significant efforts have been made to find designs simple enough to be easily built and controlled, in order to obtain practical systems [10], [11], particularly in human prosthetics. To overcome the mitiged success of the early designs, mainly due to the cost of the control architecture needed for complex mechanical systems with often more than ten actuators plus many sensors, a special emphasis has been placed on the reduction of the number of degrees of freedom (DOFs), thereby decreasing the number of actuators. In particular, the SSL hand [12], the Graspar hand [13], the DIES-DIEM hand [14], the Cassino finger [15], and the TBM hand [16] have followed this path. On the other hand, very few prototypes involve a smaller number of actuators without decreasing the number of DOFs. This approach, namely, underactuation, can be implemented through the use of passive elements like springs or mechanical limits leading to a mechanical adaptation of the finger to the shape of the object to be grasped [17]–[22]. A similar approach consists of using elastic phalanges, which increase the adaptation capability but decrease considerably the strength of the grasp [23], [24]. Another way to consider shape adaptation is to use tentacle-like fingers [25].