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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.

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web site: wwwrobot.gmc.ulaval.ca/recherche/themeO4~a.ht11il A b s t r a c t This paper studies the force capability of a particular class of underactuated fingers. Force capability is defined as the ability to create an external wrench onto a fixed object. The concept of underactuation in robotic fingers, with fewer actuators than degrees of freedom (DOF) through the use of springs and mechanical limits, allows the hand to adjust itself to an irregularly shaped object without complex control strategy and numerous sensors. However, in some configurations, the force distribution in an underactuated finger can degenerate. The finger can no longer apply forces on the object, leading in some cases to the ejection of the latter from the hand. This paper focuses on a 2-DOF finger and studies its ability to seize objects with a secure grasp.

In this paper, a methodology is proposed for the analysis of the force capabilities of connected differential mechanisms. These systems are the key elements used to extend the principle of underactuation in grasping from the fingers to the hand itself. The concept of underactuation in robotic grasping-with fewer actuators than degrees of freedom (DOF)-allows the hand to adjust itself to an irregularly shaped object without complex control strategies and sensors. Several technological solutions have been proposed in the past but no theoretical background has been provided to analyze their characteristics, especially with respect to the forces generated. The purpose of this paper is to provide such a theoretical foundation and to illustrate its usefulness with examples applied to grasping. First, several differential elements are presented and studied. Second, a mathematical method to obtain the output force capabilities of connected differential mechanisms is presented. Finally, the technique presented is applied to two types of underactuated robotic hands.

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