E. Rimon and J. W. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. J. of Robotic Systems, 12(6):433--451, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in the This work was supported in part by the National Science Foundation under DMI 0010069. Research funding was also provided by Adept Technology, and California State MICRO Grant 00 032. Taylor expansion results in a decrease in distance from some C obstacle in contact with the part. [20] shows that generic planar parts can be immobilized (secondorder) with three frictionless contacts if they are placed with infinite precision. Ponce et al. [17] give an algorithm to compute such configurations. 20] also gives a sufficient condition for immobility using two fingers when contacting ....

....results in a decrease in distance from some C obstacle in contact with the part. 20] shows that generic planar parts can be immobilized (secondorder) with three frictionless contacts if they are placed with infinite precision. Ponce et al. [17] give an algorithm to compute such configurations. [20] also gives a sufficient condition for immobility using two fingers when contacting jaws have the necessary curvature. Their analysis is for a smooth body with a unique normal at the point of contact. For force closure grasps with friction, Faverjon and Ponce [6] compute grasps for curved parts ....

Elon Rimon and Joel W. Burdick, New Bounds on the Number of Frictionless Fingers Required to Immobilize 2D Objects, IEEE International Conference of Robotics and Automation, pp 751-757, 1995.

....ON ROBOTICS AND AUTOMATION, TO APPEAR 5 such characterizations of manipulation primitives. Other related results in manipulation include the demonstration of the controllability of a ball rolling on a plane or another ball [12] bounds on the number of fingers necessary for a grasp [13] 14] [15]; the classification of orientable parts by sensorless parallel jaw grasping sequences [5] and the proof that a one joint robot operating above a fixed speed conveyor is sufficient to position and orient polygonal parts by pushing [6] Our work on characterizing controllable polygons in terms of ....

E. Rimon and J. W. Burdick, "New bounds on the number of frictionless fingers required to immobilize planar objects," Journal of Robotic Systems, vol. 12, no. 6, pp. 433--451, 1995.

....space. Higher order analyses can be used to reduce the number of fingers and thrusters needed. In Proposition 3 we proved that by using Lie brackets, i.e. motion derivatives, the number of thrusters required for smalltime local controllability is reduced to three. Rimon and Burdick [31] have recently shown that contact curvature, i.e. shape derivative, may be used to decrease the number of fingers required for complete immobilization. In particular, they showed that three point fin y x y x (a) b) Figure 2: Three finger grasps of two different objects. By a first order ....

....along the x axis is impossible, and the object is completely immobilized. gers are sufficient for form closure provided their contact normals positively span the plane and intersect at a single point C, and the centers of curvature of the perimeter of the body at the contacts do not all lie at C ([31], Proposition 4.1) Higher order shape derivatives (not just curvature) can be used in determining form closure (Figure 2) Bracket terms of higher order than those used in the proof of Proposition 3 do not create linearly independent vector fields. 3.2 Dynamic pushing Dynamic pushing is ....

E. Rimon and J. W. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. Journal of Robotic Systems, 12(6):433-- 451, 1995.

....of manipulation primitives. Other related results in manipulation include the demonstration of the controllabilityof a ball rolling on a plane or another ball (Li and Canny [5] bounds on the number of fingers necessary for a grasp (Mishra et al. 9] Markenscoff et al. 8] Rimon and Burdick [12]) the classification of orientable parts by sensorless parallel jaw grasping sequences (Goldberg [4] and the proof that a single joint operating above a fixed speed conveyor is sufficient to position and orient polygonal parts by pushing (Akella et al. 1] In the next section we provide ....

E. Rimon and J. W. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. Journal of Robotic Systems, 12(6):433--451, 1995.

....in analyzing and planning manipulation by controlled slippage. A recent extension of the classical notion of form closure is the so called immobilization problem, where the secon order effects of the curvature of the surfaces are taken into account, to provide more detailed results (see e.g. [Rimon and Burdick, 1993 and 1995]) The analysis of form closure is intrinsically geometric, and does not take into account the kinematics and characteristics of the end effector. On the other hand, the concept of force closure is often used with the intuitive meaning that motions of the grasped object are completely (or ....

Rimon, E., and Burdick, J. W.: "New bounds on the number of frictionless fingers required to immobilize 2D objects", Proc. IEEE Int. Conf. on Robotics and Automation, pp. 751--757, 1995.

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E. Rimon and J. W. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. J. of Robotic Systems, 12(6):433--451, 1995.

....measure can be used by any compliance model. Third, the quality measure is valid for grasps of 2D and 3D objects by any number of fingers. In particular, it is known that curvature e#ects can significantly reduce the number of frictionless fingers or fixtures required to stably grasp an object [32]. If desired, the sti#ness quality measure can automatically include first order e#ects (i.e. finger positions and contact normal directions) with second order e#ects (i.e. surface curvature at the contacts) in a single measure. The quality measure is thus useful for assessing in a uniform way the ....

E. Rimon and J. Burdick, "New bounds on the number of frictionless fingers required to immobilize planar objects," J. Robotic Systems, vol. 12, no. 6, pp. 433--451, 1995.

....problem and have proposed algorithms based on first order mobility theories (see [2] and [15] for example) Our second order mobility results suggest that many objects can be immobilized with substantially fewer numbers of fixtures than previously thought possible. In a sequel to this paper [21] (written after this paper was submitted) we indeed establish the new bounds for planar objects. In Ref. 12] we also showed by way of analysis and examples that the e#ectives sti#ness of grasps that rely upon second order e#ects can be comparable to those employing first order e#ects. Moreover, ....

E. Rimon and J. W. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. Journal of Robotic Systems, 12(6):433-- 451, June 1995.

....which allows us to analyze the effects of contact geometry on stability, as well as the relative contribution of first and second order effects to overall grasp stiffness. Second order effects have recently been suggested as a means to reduce the number of fingers needed to fixture an object [14]. An example shows that these second order effects can be practically important. 2 Background A grasp or fixturing arrangement consists of an object B contacted by m fingers A 1 ; Am . We assume that the contacts are frictionless, and that the boundaries of the bodies near the contact ....

E. Rimon and J. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. J. Robotic Systems, 12(6):433--451, 1995.

....that 4 contact points suffice to immobilize generic 2D objects, and 7 suffice to immobilize generic 3D objects. Czyzowicz et. al (1991) 1] have shown that generic 2D and 3D polygonal objects could be immobilized respectively by 3 and 4 frictionless point contacts. More recently, Rimon and Burdick [14] have shown that any 2D polygonal or smooth object can immobilized with 3 convex fingers (some fingers might have to be flat) They were also able to overcome the limitation of the analysis in [1] to polygons without parallel edges. Further, they have shown that if the finger curvature can be ....

E. Rimon and J. W. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. J. Robotic Systems, 12(6):433--451, June 1995.

....model as a special case. Third, the quality measure is valid for grasps of 2D and 3D objects by any number of fingers. In particular, it is known that curvature e#ects can significantly reduce the number of frictionless fingers or fixtures required to stably grasp an object. An adaptation of Ref. [18] yields that 3 convex fingers su#ce to stably grasp almost any 2D object, and 4 convex fingers seem to su#ce to stably grasp almost any 3D object. The sti#ness quality measure automatically includes first order e#ects (i.e. finger positions and contact normal directions) with second order ....

E. Rimon and J. Burdick, "New bounds on the number of frictionless fingers required to immobilize planar objects," J. Robotic Systems, vol. 12, no. 6, pp. 433--451, 1995.

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E. Rimon and J. W. Burdick. New bounds on the number of frictionless fingers required to immobilize planar objects. J. of Robotic Systems, 12(6):433--451, 1995.

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