E. Rimon and J. W. Burdick, "Mobility of bodies in contact---i: A new nd order mobility index for multiple-finger grasps," IEEE Transactions on Robotics and Automation, vol. 14, no. 5, pp. 696--708, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....capable of preventing any motion due to external forces and torques. This is captured by the dual notions of form and force closure that constitute the traditional theoretical basis for grasp planning [2] 3] 4] Recently, Rimon and Burdick have introduced the notion of second order immobility [5], 6] and shown that certain equilibrium grasps of a part which do not achieve form closure effectively prevent any finite motion of this part through curvature effects in configuration space. We introduced in [7] 8] the more general notion of inescapable configuration space region (or ICS) as ....

....shown that certain equilibrium grasps of a part which do not achieve form closure effectively prevent any finite motion of this part through curvature effects in configuration space. We introduced in [7] 8] the more general notion of inescapable configuration space region (or ICS) as shown in [5], 6] an object is immobilized when it rests at an isolated point of its free configuration space; moving the fingers in an appropriate way transforms this isolated point into a compact region of free space (the ICS) that cannot be escaped by the object. ICS regions were introduced in the ....

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E. Rimon and J. W. Burdick, "Mobility of bodies in contact---i: A new nd order mobility index for multiple-finger grasps," IEEE Transactions on Robotics and Automation, vol. 14, no. 5, pp. 696--708, 1998.

....force closure, requiring 2 as little positional accuracy from the robot as possible. This approach has been generalized to handle various numbers of fingers and different object geometries in [3, 7, 27, 29, 30, 31] Recently, Rimon and Burdick have introduced the notion of second order immobility [36, 37, 38] and shown that certain equilibrium grasps (or fixtures) of a part which do not achieve form closure effectively prevent any finite motion of this part through curvature effects in configuration space. They have given operational conditions for immobilization and proven the dynamic stability of ....

....actually achieves equilibrium, we compute the values of the coefficients i for i = 1; 2; 3. If they are all positive, then equilibrium is achieved. 2.1. 3 Immobility Rimon and Burdick have formalized the notion of immobilizing grasps in terms of isolated points of the free configuration space [36, 37, 38] (see also related work by Czyzowicz, Stojmenovic and Urrutia [8] and Mirtich and Canny [21] They have shown that equilibrium grasps that do not achieve 11 form closure may still immobilize an object through second order (curvature) effects in configuration space: a sufficient condition for ....

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E. Rimon and J. W. Burdick. Mobility of bodies in contact-I: A new 2 nd order mobility index for multi-finger grasps. IEEE Transactions on Robotics and Automation,

....also be capable of preventing any motion due to external forces and torques. This is captured by the dual notions of form and force closure that constitute the traditional theoretical basis for grasp planning. Recently, Rimon and Burdick have introduced the notion of second order immobility [11, 12] and shown that certain equilibrium grasps of a part which do not achieve form closure effectively prevent any finite motion of this part through curvature effects in configuration space. We introduced in [16, 17] the more general notion of inescapable configuration space region (or ICS) as shown ....

....shown that certain equilibrium grasps of a part which do not achieve form closure effectively prevent any finite motion of this part through curvature effects in configuration space. We introduced in [16, 17] the more general notion of inescapable configuration space region (or ICS) as shown in [11, 12], an object is immobilized when it rests at an isolated point of its free configuration space; moving the fingers in an appropriate way transforms this isolated point into a compact region of free space (the ICS) that cannot be escaped by the object. ICS regions were introduced in the context of ....

[Article contains additional citation context not shown here]

E. Rimon and J. W. Burdick. Mobility of bodies in contact---I: A new 2 nd order mobility index for multiple-finger grasps. IEEE Trans. Rob. Autom., 14(5):696--708, 1998.

....objects, and Wagner, Zhuang, and Goldberg [52] have proposed a three dimensional seven contact fixturing device and an algorithm for planning form closure fixtures of a polyhedron with prespecified pose. Recently, Rimon and Burdick have introduced the notion of second order immobility [44, 45, 46] and shown that certain equilibrium grasps (or fixtures) of a part which do not achieve form closure 4 effectively prevent any finite motion of this part through curvature effects in configuration space. They have given operational conditions for immobilization and proven the dynamic stability of ....

.... contacts in the plane and four contacts in the three dimensional case are sufficient to immobilize (i.e. prevent any finite motion of) a polyhedron [10] Rimon and Burdick have formalized the notion of immobilizing grasps and fixtures in terms of isolated points of the free configuration space [44, 45, 46] (see also related work by Mirtich and Canny [28] They have shown that equilibrium fixtures that do not achieve form closure may still immobilize an object through second order (curvature) effects in configuration space: a sufficient condition for immobility is that the relative curvature form ....

[Article contains additional citation context not shown here]

E. Rimon and J. W. Burdick. Mobility of bodies in contact-I: A new 2 nd order mobility index for multi-finger grasps. IEEE Transactions on Robotics and Automation,

....objects, and Wagner, Zhuang, and Goldberg [33] have proposed a three dimensional seven contact fixturing device and an algorithm for planning form closure fixtures of a polyhedron with pre specified pose. Recently, Rimon and Burdick have introduced the notion of second order immobility [28, 29, 30] and shown that certain equilibrium grasps (or fixtures) of a part which do not achieve form closure effectively prevent any finite motion of this part through curvature effects in configuration space. They have given operational conditions for immobilization and proven the dynamic stability of ....

.... contacts in the plane and four contacts in the three dimensional case are sufficient to immobilize (i.e. prevent any finite motion of) a polyhedron [7] Rimon and Burdick have formalized the notion of immobilizing grasps and fixtures in terms of isolated points of the free configuration space [28, 29, 30]. They have shown that equilibrium fixtures that do not achieve form closure may still immobilize an object through second order (curvature) effects in configuration space: a sufficient condition for immobility is that the relative curvature form associated with an essential equilibrium 1 ....

E. Rimon and J. W. Burdick. Mobility of bodies in contact---i: A new 2 nd order mobility index for multiple-finger grasps. In IEEE Int. Conf. on Robotics and Automation, San Diego, CA, May 1994.

....a simple three dimensional modular fixturing device and present an algorithm for enumerating all of the immobilizing fixtures of a polyhedral object that can be achieved with this device and four frictionless contacts. Our approach is based on the second order mobility theory of Rimon and Burdick [19, 20, 21]. 1 Introduction We consider the problem of computing frictionless immobilizing fixtures of a three dimensional (3D) polyhedral object. We propose a simple fixturing device (Fig. 1) which is a direct extension of the two dimensional (2D) fixturing vise proposed by Wallack and Canny [25, 26] it ....

.... device and corresponding algorithm proposed by Wagner, Zhuang, and Goldberg [24] In contrast with these approaches, all based on the concepts of form and force closure [18] the technique presented in this paper is based on the notion of second order immobility introduced by Rimon and Burdick [19, 20, 21]. Immobility can be achieved with fewer fingers than form or force closure, and we exploit this fact to design an efficient fixture planning algorithm. Section 2 reviews the notions of equilibrium, form and force closure, and second order immobility, and it presents a simple sufficient condition ....

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E. Rimon and J. W. Burdick. Mobility of bodies in contact-I: A new 2 nd order mobility index for multifinger grasps. In IEEE Int. Conf. Robot. Autom., pp. 2329-2335, San Diego, CA, 1994.

....grasps which are not form closure actually immobilize the grasped object: for example three frictionless fingers positioned at the centers of the edges of an equilateral triangle cannot prevent an infinitesimal rotation of the triangle about its center of mass, yet prevent any finite motion. See [7, 34, 50, 51] and Section 5 for discussions of this phenomenon. 2 These systems of wrenches are called strong force closure systems by Trinkle [57] Of course, as noted before, his notion of force closure is different from ours. n f f n (a) b) x x C Figure 1: Coulomb friction: the friction cone C of (a) ....

....object. Czyzowicz, Stojmenovic and Urrutia have recently shown that three fingers in the plane and four fingers in the three dimensional case are sufficient to immobilize a polyhedron, with finger arrangements corresponding to concurrent grasps [7] New techniques developed by Rimon and Burdick [50, 51] may allow us to decide whether the other two types of equilibrium grasps studied in this paper can also be used to immobilize an object in the absence of friction. More generally, it would be interesting to evaluate the quality of frictionless grasps achieved by a number of fingers between four ....

E. Rimon and J. W. Burdick. Mobility of bodies in contact---i: A new 2 nd order mobility index for multiple-finger grasps. In IEEE Int. Conf. on Robotics and Automation, San Diego, CA, May 1994.

....two cases: starting from either preloading finger forces or object displacement. Consider specifying the preloading finger forces. Then by inverting the functions f i subject to the constraint (8) we can obtain ffi i0 . Quite often, as is the case with generic 2 , 3 and 4 fingered planar grasps [15], 10] the specification of the sum of the finger forces f T = P m i=1 f i (ffi i0 ) uniquely determines the magnitude of individual finger forces. Then the preloading overlaps are functions of a single variable f T . We may also measure B s configurations, denoted by q init and q 0 , before ....

....As k L rel k decreases (as the contacting surfaces achieve a better match) the stabilizing second order effects become quite significant. In particular, when the two surfaces fit sufficiently closely, the stabilizing second order effects can become comparable with first order effects. In [15] it was shown that curvature effects could be used to reduce the number of fixtures needed to immobilize, or fixture, an object. This analysis shows that by proper selection of the fixtures curvature, fixtures with fewer contacts can still be sufficiently stiff. The following corollary applies ....

E. Rimon and J. W. Burdick. Mobility of bodies in contact--- i: A new 2 nd order mobility index for multiple-finger grasps. In Proc. Int. Conf. on Robotics and Automation, pages 2329-- 2335, San Diego, CA, May 1994.

....the gravity mobility index. Further, as shown in Section 5, we can use these results to develop engineering rules of thumb which are useful in the applications described above. Finally, we will point out analogies between our results and the second order mobility theory developed in [8] and [9]. 2 Configuration Space Review We use a configuration space (c space) based approach, as outlined in [8, 9] to analyze the stability of B about its contact configuration. The rigid object, B, and the obstacles (or finger) A 1 ; A k , are located in an n dimensional physical space, W ....

.... rules of thumb which are useful in the applications described above. Finally, we will point out analogies between our results and the second order mobility theory developed in [8] and [9] 2 Configuration Space Review We use a configuration space (c space) based approach, as outlined in [8, 9], to analyze the stability of B about its contact configuration. The rigid object, B, and the obstacles (or finger) A 1 ; A k , are located in an n dimensional physical space, W = IR n (n = 2 or 3) For our stability analysis, we can focus on the c space of B, rather than the ....

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E. Rimon and J. W. Burdick. Mobility of bodies in contact: A new 2 nd order mobility index for multiplefinger grasps. In Proc. IEEE Int. Conf. on Robotics and Automation, pages 2329--2335, San Diego, CA, May 1994.

....force closure) and vice versa. We also introduce a novel 2 nd order force closure definition, and show that our 2 nd order form closure definition is dual to 2 nd order force closure. Our analysis and discussion is based on a recent mobility theory which has been developed by the authors [10, 11, 12, 13]. This theory determines the mobility of a smooth object, B, held in frictionless contact by smooth rigid and stationary finger bodies or fixtures A 1 ; A k . Our mobility analysis (which is reviewed in Section 3) is formulated in configuration space (cspace) 2 Relation to Previous ....

.... 1 ; k such that 0 = 1 n 1 (q 0 ) Delta Delta Delta k n k (q 0 ) i 0 and P k i=1 i = 1: 2) We assume that each n i (q 0 ) in (2) is essential for the grasp, meaning that the origin cannot be positively spanned with any subcollection of fn 1 (q 0 ) n k (q 0 )g [10]. Grasps are generically essential in the planar case for k = 2; 3; 4 and in the spatial case for k = 2; 7. It can be shown that at a k fingered equilibrium grasp, M 1 1; k (q 0 ) forms a subspace [12] This subspace consists of 1 st order motions which are rollslide with respect to ....

[Article contains additional citation context not shown here]

E. Rimon and J. W. Burdick. Mobility of bodies in contact: A new 2 nd order mobility index for multiplefinger grasps. In Proc. IEEE Int. Conf. on Robotics and Automation, pages 2329--2335, San Diego, CA, May 1994.

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