F. Reuleaux. The Kinematics of Machinery. Macmillan, 1876. Republished by Dover, New York, 1963.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....We also assume that all contacts are interior to an edge of the part we do not allow a fixture element to contact a part vertex since such contacts may damage the part. A fixture is acceptable if it provides form closure, which is a kinematic condition that prevents any infinitesimal motion [Reuleaux 1876] Results from linear algebra show that at least 4 wrenches are necessary for form closure. Markenscoff, Ni, and Papadimitriou 1990] showed that 4 wrenches are sufficient for any piecewise smooth compact connected planar body, excluding surfaces of revolution. We consider two types of modular ....

....in robotics. The goals of both are similar: fixing an object kinematically by means of a suitable set of contacts. The primary difference is that modular fixtures place restrictions on the relative location of contacts due to the underlying lattice. The century old definition of form closure [Reuleaux 1876] captures the intuitive function of a fixture. A set of contacts provides form closure if infinitesimal part motion is completely constrained; equivalently, the set of contacts is able to resist arbitrary forces and torques on the part. Each contact provides a wrench: a force with a point of ....

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F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

....is again the description size of the output. 1 Introduction Many manufacturing operations, such as machining, assembly, and inspection, require objects to be xtured, that is, to be held in such a way that they can resist all external wrenches. The concept of form closure, formulated by Reuleaux [13] in 1876, provides a sucient condition for constraining, despite the application of an external wrench, all nite and in nitesimal motions of a rigid object by a set of contacts along its boundary. Any motion of an object in form closure has to violate the rigidity of the contacts. Markensco et ....

....want to determine all placements of these points (and lines) in contact with the boundary of P such that these frictionless contacts achieve form closure or 2nd order immobility. Analysis of these placements or grasps can be performed in several ways. An intuitive method for form closure analysis [13] considers grasps in the two dimensional space of the part itself. Its graphical nature will allow us to translate the problem of nding all form closure grasps into a geometric searching problem. A similar translation can also be made for 2nd order immobility grasps. Before we outline the ....

F. Reuleaux, The Kinematics of Machinery, Macmilly and Company (1876); republished by Dover (1963).

....work. 2 Related Work Fixturing is closely related to grasping. The purpose in both cases are to immobilize the part. Modular fixturing is however different from grasping because the locators are restricted to the discretized holes on the regular lattice. The form closure condition defined by [23] gives the sufficient condition for immobilization. A set of contacts is said to provide form closure if infinitesimal motions are prohibited. Equivalently, a set of contacts provides form closure if the corresponding set of wrench vectors positively span the wrench space. In planar case, the ....

F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

....used tool in industrial and automated manufacturing processes. A fixture is a device that locates and holds parts during assembly, inspection, or machining. It usually consists of a number of fixed locators and a flexible clamp [8] Conventional fixtures are designed to hold a part in form closure [9]: the fixture geometry creates kinematic constraints that prevent any infinitesimal motion of the part. In contrast, force closure [10] requires that the contacts be able to withstand any force or torque applied to the part. For fixturing of micro parts we are interested in fixtures that provide ....

F. Reuleaux, The Kinematics of Machinery, Macmilly and Company, 1876. Republished by Dover in 1963.

....using first order theories that are based on notions of instantaneous force and velocity [5, 11, 22, 32] For example, Ohwovoriole and Roth [22] describe the relative motions of bodies in contact in terms of Screw Theory, which is a first order theory. Using first order notions, Reuleaux (1876) [23], Somo# (1900) 30] Mishra et. al (1987) 20] and Markensco# et. al (1990) 13] derived bounds on the number of frictionless point contacts required for force closure, which is one means to immobilize an object. However, first order theories are often inadequate in practice. For example, ....

....su#cient for complete immobility of B. It is known that almost all 2D or 3D objects can be held in a frictionless force closure grasp (which is equivalent to first order immobility) by m 1 contact points, where m is the c space dimension. Thus, 4 contacts su#ce for 2D grasps and 7 for 3D grasps [13, 23, 30]. Moreover, m 1 is the smallest possible number when only the point contact aspect of the fingers is considered. However, our second order mobility theory suggests that objects can be immobilized with less than m 1 frictionless contacts if curvature e#ects are taken into account. We say that an ....

F. Reuleaux. The Kinematics of Machinery. Macmillan 1876, republished by Dover, NY, 1963.

....in fixturing literature over the past years has not always been consistent. Here we discuss a few different notions on immobility of objects and show how our definition of form closure, which we will use in the rest of this paper, fits in. Several authors have discussed form closure and immobility [3, 11, 24, 26, 27]. Initially Reuleaux [25] used the term force closure to describe immobilization (equilibrium) of an object that requires the application of an externally applied wrench. He defined form closure on a body as an equilibrium that is maintained despite the application of any possible externally ....

F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

....been studied using first order theories that are based on notions of instantaneous force and velocity. For example, Ohwovoriole and Roth [12] describe the relative motions of bodies in contact in terms of Screw Theory, which is a first order theory. Using first order notions, Reuleaux (1876) [13], Somoff (1900) 19] Mishra et. al (1987) 11] and Markenscoff et. al (1990) 7] derived bounds on the number of frictionless point contacts required for force closure, which is one means to immobilize an object 1 . However, first order theories are often inadequate in practice. For example, ....

....for complete immobility of B. It is known that almost all 2D or 3D objects can be held in frictionless force closure grasp (which is equivalent to 1 st order immobility) by m 1 contact points, where m is the c space dimension. Thus, 4 contact points suffice for 2D grasps and 7 for 3D grasps [7, 13, 19]. Moreover, m 1 is the smallest possible number when only the point contact aspect of the fingers is considered. However, our 2 nd order mobility theory suggests that objects can be immobilized with less than m 1 frictionless fingers if curvature effects are taken into account. We say that an ....

F. Reuleaux. The Kinematics of Machinery. Macmillan 1876, republished by Dover, NY, 1963.

....Figure 1: An example fixture with an edge fixel, a locator and a clamp. 1 Introduction Many manufacturing operations, such as machining, assembly, and inspection, require constraints on the motions of parts or subassemblies of parts [4, 6] The concept of form closure is over a century old [15] and refers to constraining, despite the application of an external wrench (force and moment) all motions of a rigid object (including infinitesimal motions) by a set of contacts on the object; any motion of an object in form closure has to violate the rigidity of the contacts. Therefore, the ....

F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

....We also assume that all contacts are interior to an edge of the part we do not allow a fixture element to contact a part vertex since such contacts may damage the part. A fixture is acceptable if it provides form closure, which is a kinematic condition that prevents any infinitesimal motion [Reuleaux 1876] Results from linear algebra show that at least 4 wrenches are necessary for form closure. Markenscoff, Ni, and Papadimitriou 1990] showed that 4 wrenches are sufficient for any piecewise smooth compact connected planar body, excluding surfaces of revolution. We consider two types of modular ....

....in robotics. The goals of both are similar: fixing an object kinematically by means of a suitable set of contacts. The primary difference is that modular fixtures place restrictions on the relative location of contacts due to the underlying lattice. The century old definition of form closure [Reuleaux 1876] captures the intuitive function of a fixture. A set of contacts provides form closure if infinitesimal part motion is completely constrained; equivalently, the set of contacts is able to resist arbitrary forces and torques on the part. Each contact provides a wrench: a force with a point of ....

[Article contains additional citation context not shown here]

F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

....planar grasps. However, because the three contacts are sliding, there are only have three constraining unisense wrenches. Therefore, form closure is impossible. Instead, the contacts are maintained by the action of the external wrench; the situation referred to as force closure by Reuleaux [33] and Salisbury [35] Figure 4 illustrates the graphical interpretation of the conditions stated in the Corollary and embodied in inequalities (35) and (36) It requires knowledge of the lines of action and the directions of the contact forces, which are known assuming that the joint velocity ....

F. Reuleaux. The Kinematics of Machinery. Macmillan, 1876. Republished by Dover, New York, 1963.

....modeling the compliance and friction properties at the contacts [14] Also, the kinematic constraints associated with each rolling contact are nonholonomic and thus further complicate planning. In this paper, we assume that the three dimensional 1 We use Reuleaux s definition of force closure [12]. workpiece is frictionless, the fingers are rigid, and that inertial effects are negligible. This leads to a holonomic model that predicts motions uniquely. While the frictionless assumption is not appropriate in many potential grasping and whole arm manipulation applications, we have chosen it ....

F. Reuleaux. The Kinematics of Machinery. Macmillan, 1876. Republished by Dover, New York, 1963.

....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 Work The history of force form closure analysis dates back to the work of Reuleaux (1876) [9] and Somoff (1900) 15] More recent analysis dates to the work of Lakshminarayana [3] Numerous investigators have provided various equivalent definitions of force closure. However, all of these definitions are based on what we term 1 st order notions of velocity and force. Our definition of 2 ....

....the concepts of force and form closure have been used to analyze grasping [7, 16] fixturing [6] and whole arm manipulation [17] One fundamental application of the force form closure concept is the issue of the number of frictionless contacts that are required to immobilize an object. Reuleaux [9] found that at least 4 frictionless point contacts are required to immobilize 2 dimensional (2D) objects. Somoff [15] found that at least 7 frictionless contact points are required to immobilize 3 dimensional (3D) objects. Much later, Markenscoff et. al (1990) 4] established that 4 contact ....

F. Reuleaux. The Kinematics of Machinery. Macmillan 1876, republished by Dover, NY, 1963.

....closely related to grasp planning in robotics. The goals of both are similar: fixing an object kinematically by means of a suitable set of contacts. A primary difference is that modular fixtures place restrictions on the relative arrangement of contacts. The century old definition of form closure [12] captures the intuitive function of a fixture. A set of contacts provides form closure if infinitesimal part motion is completely constrained; equivalently, the set of contacts is able to resist arbitrary forces and torques on the part. Each contact provides a wrench: a force with a point of ....

....rotation, it is always possible to shift P horizontallyand vertically such that the four points defining the closure are each close enough to a lattice point, at which we could anchor a fixel applying a force normal to P at that point. Finally, note that 4 contacts are necessary according to [12] . Now we generalize this result to non point (round) fixels. Theorem 4 Let P be a rectilinear part with all edges of length 1 unit. Then there always exists a fixture for round fixels using at most 4 clamps. Furthermore this bound is tight. Proof. Let P be P grown by the fixel radius using ....

F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

....1 We study the specific case of only one manipulated object, but the extension to multiple objects is straight forward. 2 Nguyen refers to frictional form closure[4] as force closure. However, we reserve the use of the term force closure for situations originally identified by Reuleaux [32] The most general formulation of the manipulation planning problem in which sliding was allowed, was published by Li and Canny [22] However, in their formulation, they assumed that the manipulated object could only contact the hand on the most distal link of each finger and they have not ....

....quasistatic, multi rigid body systems with Coulomb friction acting at the contact points. These cells are 10 Recall that Nguyen refers to frictional form closure [4] as force closure [27] However, we reserve the use of the term force closure for situations originally identified by Reuleaux [32]. n dimensional subsets of C space in which paths corresponding to whole arm manipulation tasks which can be executed without jamming. Due to the generality of the systems considered here, our jamming results are more general that previous ones for quasistatic systems. In specific, our ....

F. Reuleaux. The Kinematics of Machinery. Macmillan, 1876. Republished by Dover, New York, 1963.

....describe the motion spaces and the computation of restraints for translational and rotational motion, respectively. The proposed analysis is applied to an example in section 5. Section 6 summarizes this paper and points out directions for future research. 2 Motion Constraints from Contact Reuleaux[9] analyzed the effect of point contact on translational and rotational motion of planar objects. A T T a N (b) N A B a (a) b T T a N N A (c) l r A T T a N N P O Q (d) b Figure 1: Reuleaux s analysis of restraints (a) A planar object A with contact at a, b) Restraints to ....

F. Reuleaux, The Kinematics of Machinery. Macmillan 1876, Republished by Dover, 1963.

....motion is disallowed is referred to by M d . Thus each additional mating surface element reduces the space M p and expands the space M d such that the following relations are satisfied M a = M p [ M d M p M d = 1) After all effects have been considered, M p is the solution space. Reuleaux [7] identified the kinematic pair and studied the geometric form of these pairs. He observed that there exists some general principle underlying the spatial arrangement of contact surfaces so as to maintain their mutual positions. He analyzed the effect of point contact on translational and ....

....the virtual work be positive, inequalities are obtained, one for each wrench. These when solved give the unknown twist coordinates. Thus the displacement that the body is allowed to incur in the presence of the contacts can be obtained. In dealing with planar motion, the method used by Reuleaux [7] is simpler and provides identical results. The simplicity is gained by analyzing directly the effect of contact on permissible motion (as against first obtaining forces of restraint due to contact and then (a) b) directions disallowed due to contact face A face A d p Object O 1 Object O 2 f f ....

F. Reuleaux, The Kinematics of Machinery. Macmillan 1876, Republished by Dover, 1963.

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F. Reuleaux. The Kinematics of Machinery. Macmillan, 1876. Republished by Dover, New York, 1963.

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F. Reuleaux, The Kinematics of Machinery . Macmillan, London (1876), republished by Dover, New York, NY (1963).

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F. Reuleaux. The Kinematics of Machinery. Macmillan, 1876. Republished by Dover, New York, 1963.

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Reuleaux, F. 1876. The Kinematics of Machinery. London: Macmillan. (republished in 1963 by Dover, New York).

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F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

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F. Reuleaux. The Kinematics of Machinery. Macmillan, 1876. Republished by Dover, New York, 1963.

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F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

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F. Reuleaux. The Kinematics of Machinery. Macmilly and Company, 1876. Republished by Dover in 1963.

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F. Reuleaux. The Kinematics of Machinery. Macmillan 1876, republished by Dover, NY, 1963.

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