IEEE TRANSACTIONS ON ROBOTICS 1 Stable Precision Grasps by Underactuated Fingers Gert A. Kragten, Mathieu Baril, Cl´ ement Gosselin, and Just L. Herder Abstract—The ability of underactuated hands to grasp small objects is very limited, because the precision grasp is normally unstable. The goal of this paper is to achieve stable precision grasps by means of simple design modifications of the distal phalanges of the fingers. These modifications comprise the curving of the contact area of the distal phalanx, the application of a mechanical limit to prevent hyper-extension of the distal phalanx, and the application of a compliant joint between the proximal and distal phalanges. A model is developed to calculate the boundary conditions of the finger dimensions in order to achieve stable precisions grasps for different object sizes. An experimental setup is used to test the grasp stability and to verify the calculated results. It is concluded that stable precision grasps exist for the combination of concavely curved distal phalanges with a mechanical limit or with a compliant joint, if the boundary conditions of the finger dimensions are satisfied. I. I NTRODUCTION Underactuated robotic hands can grasp various objects, because the fingers adapt themselves to the shape of the objects by their mechanical behavior. Underactuation means that the number of actuators is less than the degrees of freedom. Numerous examples in the literature show that this principle can lead to adaptive hands that are relatively cheap, lightweight and easy to control compared to fully actuated hands, e.g. [1], [2], [3]. The adaptation of the fingers to the objects is especially beneficial to envelope objects in a so-called power grasp [4]. However, sometimes enveloping objects is not possible, for instance, when small objects are grasped, or when objects are approached from above. In such cases the objects need to be grasped by the distal phalanges only. In literature this is normally called a precision grasp [4], [5], a pinch grasp [6], or a palmar or tip grasp [7]. The term precision grasp will be used throughout this paper to refer to a grasp equilibrium that is achieved by the distal phalanges only. It is reported that a precision grasp is difficult to achieve by underactuated fingers, e.g. [8], [9], [10]. It was shown in [11] that this is caused by the instability of a precision grasp equilibrium, where unstable means that the potential energy of the hand and object at this equilibrium point is not a local minimum. This means that grasping small objects by underactuated hands is impossible, unless specific design modifications are applied. Generally, a compliant, frictional contact material − like the skin of a human finger − can improve the capability to obtain a precision grasp. Some other solutions have been Gert A. Kragten and Just L. Herder are with the Dept. of BioMechanical Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands (email: g.a.kragten@tudelft.nl; j.l.herder@tudelft.nl, fax: 0031-15-2784713). Mathieu Baril and Cl´ ement Gosselin are with the D´ epartement de g´ enie m´ ecanique, Pavillon Adrien-Pouliot, 1065 avenue de la M´ edecine Universit´ e Laval, Qu´ ebec, (Qu´ ebec) Canada, G1V 0A6 (email: math- ieu.baril.4@ulaval.ca; gosselin@gmc.ulaval.ca, fax: 418-656-7415). proposed to achieve a precision grasp by underactuated fingers. The SARAH [8] and the TWIX-hand [12] make use of an additional mechanism to keep the distal phalanges parallel to each other as long as no contact with an object is encountered. The adaptive hand of RobotIQ [13] can actively switch between a mode for a precision grasp between parallel distal phalanges, and a mode for a power grasp where the objects are enveloped. The addition of an extra mechanism to the fingers or the active switching between modes complicates the design, which is not desired. Also triggered mechanisms are proposed as a less complicated solution to keep the distal phalanges parallel [14], [15]. However, sufficient contact friction and accurate grasp planning remain necessary to stably grasp the objects between parallel phalanges. If these conditions are not satisfied, a stable precision grasp does not exist. The goal of this paper is to investigate the achievement of stable precision grasps by underactuated fingers by means of simple design modifications. The effect of these design modifications to the grasp stability is studied by a model that considers the fingers and object as a conservative system. This means that the potential energy must be a local minimum at a precision grasp equilibrium. The results of this model and the effectiveness of the proposed design modifications are verified by experiments. The relevance of this work is that the existence of the precision grasp does not depend on contact friction anymore. In addition, accurate grasp planning is not necessary, because there will be a stability area where the objects are attracted towards the stable precision grasp equilibrium. Finally, it leads to understanding of the stability of underactuated fingers and the grasped objects. The structure of the paper is as follows. Section II introduces a model to calculate the stability of a precision grip between straight phalanges. Three design modifications for the underac- tuated fingers are then proposed, and the stability of precision grasps between these fingers is calculated as a function of the design parameters. An experimental setup is described for measuring the stability. Section III provides the results of the calculated and measured stable precision configurations. In addition, it provides a visualization of the boundary conditions on the design parameters to achieve stable precision grasps. The effectiveness of the three design modifications is discussed in Section IV, followed by conclusions in Section V. II. MATERIALS AND METHODS A gripper consisting of two underactuated fingers with two straight phalanges each is taken as a reference to develop a model to calculate the grasp stability. Then, three design mod- ifications are proposed, and the model is adapted accordingly