Wilson, R.H. and Latombe, J.C., Geometric Reasoning About Mechanical Assembly, Artificial Intelligence, 71(2), 371-396, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....property is called a depth order . It need not always exist, but when it does, the product can be assembled by translating the constituent parts one after another, in the reverse of the depth order, to their target positions. Products that can be assembled in this manner are called stack products [WL94] The simplicity of the assembly process makes stack products attractive to manufacture. Computing a depth order in a given direction (or deciding that no such order exists) can be done in O(m ) time, for any 0, for a set of polygons in 3 space with m vertices in total [dBOS94] Faster ....

R.H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artif. Intell., 71:371-396, 1994.

....arcs branch out. Each arc represents an assembly operation and each node represents an assembly state. Each level in the tree is ranked so the root (disassembled state) is at the 0th rank and, as each component is assembled, the rank and level in the tree is increased by 1. In Wilson and Latombe [57], a directional blocking graph (DBG) is utilised which 21 represents the blockages encountered by each component in an assembly along contact edges with respect to a removal direction. For example in Figure 6, component 2 is blocking component 1 in the removal direction so an arrow is drawn from ....

Wilson R.H. & Latombe Jean-Claude., "Geometric reasoning about mechanical assembly", Artificial Intelligence, Vol. 71, No. 2, 1993, pp. 371-396.

....local geometry, material, and accuracy requirements. In other words, these processes localize geometric interactions and thereby avoid the combinatorics associated with global feature interactions, a wellknown source of difficulty in automated CNC machining [Gupta and Nau 1995] robotic assembly [Wilson and Latombe 1994] and similar processes. These layered processes also remove traditional manufacturing constraints, for example, fixturing requirements and tool access planning, which are often major barriers to automatic process planning and manufacturability analysis. The challenge with mechanical systems, ....

R. H. Wilson and J-C. Latombe, "Geometric reasoning about mechanical assembly," Artificial Intelligence, v 71 n 2, pp. 371-396, Dec 1994.

....We only consider their effect on the manipulated object. Hence, our work is similar in spirit to the work done in assembly sequencing and assembly maintainability studies where removal paths for assembly parts are computed without taking into account the tools required to perform the removal [17, 63]. In assembly planning, as in our case, reasoning about the required tools complicates the problem to a degree that is very Figure 2: Snapshots along a path computed by our planner for positioning a metallic belt in a pipe assembly of a car. The actuators, not shown in the figure, grasp the two ....

R. Wilson and J. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371-396, 1995.

....which we call grasping constraints or limit conditions that reflect the effect of manipulation on our object. These constraints account for deformations of the plate as manipulation by robotic arms would do. In this respect, our work is in similar spirit with work done in assembly sequencing [19]. 2.1 Grasping Constraints An elastic metal plate can be deformed either by applying forces on it or by constraining the position of a subset of its points (position of two edges for instance) These constraints are defined by grasping and give rise to limit conditions according to which the ....

R. Wilson and J. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371-396, 1995.

....application area, the reader is referred to the survey by Bose and Toussaint [2, 5] In assembly, the emphasis is on planning tasks so as to put parts together to form the final product. Interesting geometric problems arise in almost every step of automatic assembly planning. Assembly sequencing [24], part orienting [9] fixturing [18] and welding [17] are just a few of many examples. Although these manufacturing and assembly processes may be totally different from one another, some of them raise similar geometric problems that can be generally termed separability problems [22] This is ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371--396, 1994.

....the reader is referred to Bose s thesis [2] and the survey by Bose and Toussaint [4] In assembly, the emphasis is on planning tasks so as to put parts together to form the nal product. Interesting geometric problems arise in almost every step of automatic assembly planning. Assembly sequencing [27], part orienting [11] xturing [21] and welding [19] are just a few of many examples. Although these manufacturing and assembly processes may be di erent from one another, some of them raise similar geometric problems that can be generally termed separability problems [25] This is the case in ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Arti cial Intelligence, 71:371-396, 1994. 17

....automated and the interactive approach is used; they ask the user information about precedence rules, accessibility constraints and elements that can not be disassembled by simple translation. The system is made of 4 modules, only the first one is reported as fully implemented. Wilson and Latombe [80] reduced the complexity of generating assembly algortihms for 3D models to polynomial bonds trough the use of non directional blocking graphs. Most of the above planners have problems when dealing with real world assemblies, Chakrabarty and Wolter [13] propose a hierarchical approach to lessen ....

R. H. Wilson and J-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371--396, 1994.

....is a computational bottleneck in mechanical design , it is especially challenging for curved parts with multiple, changing contacts [5, 6] The current state of art in this area has left much to be desired. The input to almost all the reported automatic assembly planning systems, such as [24, 25, 16, 4], is one static state of the final assembly configuration regardless the assembly is meant to be rigid or articulated. Most work in contact analysis is dealing with planar surfaces [22, 17, 7] While the most impressive work on higher pairs 1 analysis and simulations [5, 21, 2] still need human ....

Randall Wilson and Jean-Claude Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2), December 1994.

....product recycling, and in particular, assembly planning. A lot of assembly planners use the assembly by disassembly strategy [4, 13] An assembled product exhibits more constraints on its components than in its disassembled state and hence reduces the range of motions that a planner must consider [27]. Assembly Disassembly planning had traditionally This research supported in part by NSF CAREER Award CCR 9624315 (with REU Supplement) NSF Grants IIS9619850 (with REU Supplement) ACI 9872126, EIA 9975018, EIA 9805823, and EIA 9810937, and by the Texas Higher Education Coordinating Board ....

....Board under grant ARP 036327 017. been of interest to AI researchers. The geometric approach to assembly planning originated in robotics. Automatic Planners were developed using di erent schemes amongst which is the potential eld approach of Gottschlich and Kak [9] Wilson and Latombe [27] suggested a non directional blocking graph (NDBG) for the ecient generation of assembly algorithms. Wolter [28] analyses and reports di erent schemes and data structures used in assembly planning. Constraint Languages have also been commonly used for assembly planning [29, 16] Virtual Reality ....

R. H. Wilson and J-C. Latombe. Geometric reasoning about mechanical assembly. Articial Intelligence, Elsevier Science, pages 371-396, 1994.

....modeling systems and deal predominantly with form or machining features. ffl Assembly Planning has been approached as both a geometric and symbolic reasoning problem. Geometric reasoning applied to assembly planning has focused on motion planning, fixturing, and robotic as well as human grasping [13, 28]. Symbolic approaches emphasize the generation of assembly sequences for individual components and sub assemblies as well as on the development of rules and spreadsheets to help designers create more efficient assemblies [2] Much of the existing geometric reasoning work operates on polyhedral ....

R. Wilson and J-C Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

....and document sequences of assembly. Given a CAD model of the product, the program automatically finds part topart contacts, generates collision free insertion motions, and chooses assembly order. Disassembly operations are generated using the Non Directional Blocking Graph approach discussed in [14]. A graphics workstation s hardware Z buffer is used to quickly find collisions between complex facetted models. The search space implemented in the Archimedes system is an AND OR graph of subassembly states [11] and the operations used to construct them from smaller subassemblies. The strategy is ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371-396, 1994.

....into components for ease of manufacturing during cutting, bending, and assembly. He unfolds 3D products into 2 D patterns, and identifies unfolding bend sequences that avoid collisions with tools. The motion constraints in carton folding parallel those in assembly planning. Wilson and Latombe [22] developed the non directional blocking graph representation for assembly planning by disassembly sequencing. Of related interest is work by Goldberg and Moradi [6] on assembly planning for machines that execute a pipelined series of part rotations and vertical insertions requiring only one or two ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, Dec. 1994.

....which we call grasping constraints or limit conditions that reflect the effect of manipulation on our object. These constraints account for deformations of the plate as manipulation by robotic arms would do. In this respect, our work is in similar spirit with work done in assembly sequencing [19]. 2.1 Grasping Constraints An elastic metal plate can be deformed either by applying forces on it or by constraining the position of a subset of its points (position of two edges for instance) These constraints are defined by grasping and give rise to limit conditions according to which the ....

R. Wilson and J. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371--396, 1995.

....yet interesting versions of the problem have been shown to have polynomial time and space algorithms. For example, let us consider the case of planar polygonal assemblies where the only class of motions allowed is infinite translations and where each split results in two sub assemblies [Wilson and Latombe, 1994, Latombe et al. 1996] The space of motions is described by the circle S 1 since a translation corresponds to a unit vector in the plane. Given any two parts, the set of directions along which one can be translated without colliding the other is described by a cone on the circle S 1 . This ....

Wilson, R. and Latombe, J.-C. (1994). Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371--396.

....a method to obtain the degrees of freedom of a part in an assembly from its mating constraints. Mattikalli and Khosla (1991) describe a method to obtain degrees of freedom from component mating constraints, wherein they use a unit sphere to represent the space of all available degrees of freedom. Wilson and Latombe (1994) introduce the concept of a non directional blocking graph which describes the allowed degrees of freedom after surface mating constraints have been considered. Anantha et al. 1996) describe assembly modelling by the satisfaction of geometric constraints. Ge and McCarthy (1991) characterize the ....

Wilson, Randall H.; and Latombe, Jean-Claude, "Geometric Reasoning about Mechanical Assembly", Artificial Intelligence, Vol. 71, No. 2, December 1994, pp. 371-396.

....In constructing assembly plans, one assumes the existence of such a decomposition: AND OR graphs [ 7 ] Precedence graphs [ 4 ] Backward Assembly Planning [ 13 ] Assembly Constraint Graph [ 20 ] etc. The closest approach to handling general geometries is that of Wilson and Latombe [ 19 ] , which extends the blocking graph model to identify a discretization in the translation space in two dimensions. The model works only for assembly, and is not useful in spatial reasoning, kinematics, or other tasks. Also, it is restricted to 2D and does not handle rotations. Another class of ....

Randall H. Wilson and Jean-Claude Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, v.72:1-2:371--396, November 1994.

....car apart. A classic recycling example is to strip down an old computer for a valuable part with minimal effort. Several current assembly sequence packages [10, 13] have started to offer their users the option of optimizing disassembly sequences over complexity measures such as the one we study [4, 6, 14, 18]. Unfortunately, there has been little success algorithmically for this task, and these packages currently must rely on either a brute force search through all possibilities, or on heuristic searches with no performance guarantees. Our work explains the difficulty of this task, even under much ....

R. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(1), 1995.

....by Czech Republic Grant GA CR 0194 and by Charles University Grants No. 193,194. In assembly, the emphasis is on planning tasks so as to put parts together to form the final product. Interesting geometric problems arise in almost every step of automatic assembly planning. Assembly sequencing [26], part orienting [11] fixturing [20] and welding [19] are just a few of many examples. Although these manufacturing and assembly processes may be totally different from one another, some of them raise similar geometric problems that can be generally termed separability problems [24] This is ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371--396, 1994.

....the reader is referred to Bose s thesis [3] and the survey by Bose and Toussaint [6] In assembly, the emphasis is on planning tasks so as to put parts together to form the final product. Interesting geometric problems arise in almost every step of automatic assembly planning. Assembly sequencing [27], part orienting [11] fixturing [21] and welding [19] are just a few of many examples. Although these manufacturing and assembly processes may be different from one another, some of them raise similar geometric problems that can be generally termed separability problems [25] This is the case ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371--396, 1994.

....car apart. A classic recycling example is to strip down an old computer for a valuable part with minimal effort. Several current assembly sequence packages [12, 16] have started to offer their users the option of optimizing disassembly sequences over complexity measures such as the one we study [5, 7, 17, 21]. Unfortunately, there has been little success algorithmically for this task, and these packages currently must rely on either a brute force search through exponentially many possibilities, or on heuristic searches with no performance guarantees. Our work explains the difficulty of this task, even ....

R. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(1), 1995.

....it becomes more obvious that there is a gap between the output of a mechanical designer and the input of an assembly planner. The question is: How to describe a designed assembly to an assembly planning system The input to almost all the current reported automatic assembly planning systems [17, 18, 11, 5] is one static state of the final assembly configuration regardless the assembly is meant to be rigid or articulated. The inability to represent the assembly design completely, accurately and computationally has hindered the power of an assembly planner in dealing with articulated assemblies as ....

....between gears (non surface contact) are simply determined by some translations a ij ; b ij ; c ij , where the relative gear pitch ratio is also embedded, and a rotation in SO(2) This representation of the gearbox (Figure 10) specifies precisely the articulated gearbox assembly. Figure 11 from [17] shows a nonlinearizable assembly. Using our representation, one can immediately determine it is a nonlinearizable assembly by computing the symmetry group of the contacting surfaces for each individual part under any possible motion. The result is an identity group, meaning no existing relative ....

Randall Wilson and Jean-Claude Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2), December 1994.

....in its most general form, is NP complete [27, 30, 36, 47] and thus many researchers began considering restricted, yet still interesting, versions of the problem. For many of these restricted settings, polynomial algorithms have been designed which find an assembly sequence if one exists [1, 19, 22, 43, 45]. There are also algorithms which enumerate all possible assembly sequences [12] however there may be exponentially many such sequences for a product. A logical continuation to this success is to use automated reasoning to find the best assembly sequence under certain complexity measures. In ....

....tools and to develop planners capable of finding optimal or near optimal sequences rather than just feasible sequences. Unfortunately, meeting this challenge has been difficult. Several complexity measures for assembly sequencing have been suggested, motivated strongly by industrial applications [7, 17, 45, 47]. In fact, some current software systems offer the user the option of optimizing the sequence over a choice of complexity measures [29, 40] however these systems must rely on either a brute force search of the entire space, or else A type searches without performance guarantees. The ....

R. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

.... example, some systems insert parts only along the major axes [3, 9, 10, 11] while others insert only one part at a time [2, 4] For the case of binary, monotone sequences using straightline part insertions from any direction, Wilson and Latombe presented a complete polynomial time algorithm in [12] using the non directional blocking graph (NDBG) data structure. One common thread that appears in much of the literature is the strategy of assembly by disassembly , in which an assembly sequence is generated by starting with the completed product and working backwards through disassembly steps. ....

R. Wilson and J. Latombe, "Geometric reasoning about mechanical assembly," Artificial Intelligence, vol. 71, no. 2, pp. 371--396, 1994.

....number of re orientations of the assembly. We begin by studying a graph theoretic generalization of assembly sequencing which we term virtual assembly sequencing (VAS) Much of the success in finding feasible sequences has been a result of the introduction of the non directional blocking graph [50, 52]. For a given direction of motion, the geometric model of the product can be analyzed to construct a graph which represents the blocking relationships among the parts. Once a set of such graphs has been computed, they can be analyzed to compute a feasible (dis)assembly sequence, when one exists. ....

.... operation generates a final subassembly, and two handed sequences, where every operation merges exactly two subassemblies) For many classes of motions, described by a constant number of degrees of freedom, polynomial algorithms were developed which will find an assembly sequence if one exists [22, 24, 50, 52]. Most of this success can be achieved within the framework of nondirectional blocking graphs [50, 52] and as our work is intricately related to this approach, we review these approaches in more detail in Section 3.1. It is also possible to enumerate all possible assembly sequences [16] although ....

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R. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

....the number of re orientations of the assembly. We begin by studying a graph theoretic generalization of assembly sequencing which we term virtual assembly sequencing (vas) Much of the success in finding feasible sequences has been a result of the introduction of the non directional blocking graph [74, 76]. For a given direction of motion, the geometric model of the product can be analyzed to construct a graph that represents the blocking relationships among the parts. Once a set of such graphs has been computed, it can be analyzed to compute a feasible (dis)assembly sequence, when one exists. This ....

....can be separated by a collision free motion. Once this is done, each of the resulting subassemblies can be disassembled in a similar manner. The structure of this decomposition can be represented naturally as a binary assembly tree. Figure 1. 1 gives an example of such an assembly tree, taken from [76], for a simple two dimensional product. The root of the tree represents the fully assembled product, and the children of an internal node represent two subassemblies that can be combined together to produce the larger subassembly represented by the parent. Note however, that the assembly tree only ....

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R. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

....up the parts and move them in one fixed direction the vertical direction for instance suffices to do the assembly. We ignore here and in the rest of the paper the issue of how the parts are grasped and manipulated, focusing on the inherent assemblability of the product. Wilson and Latombe [18] call products that can be assembled in this manner stack products. The simplicity of the assembly process makes stack products attractive to manufacture. See the collection edited by Homem de Mello and Lee [11] for a survey of problems and techniques in computer aided mechanical assembly ....

....and Lee [11] for a survey of problems and techniques in computer aided mechanical assembly planning. Many products, however, are not stack products, that is, a single direction in which the parts must be moved is not sufficient to assemble the product. One solution, proposed by Wilson and Latombe [17, 18], is to search for an assembly sequence that allows to move a subcollection of parts as a rigid body in any direction. Although their solution has polynomial running time (in contrast with many techniques in mechanical assembly planning) its running time is rather high in the worst case: it may ....

R. H. Wilson and J.-C. Latombe, Geometric reasoning about mechanical assembly, Artificial Intelligence 71 (1994), 371--396.

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Wilson, R.H. and Latombe, J.C., Geometric Reasoning About Mechanical Assembly, Artificial Intelligence, 71(2), 371-396, 1994.

....one exists) simple, and improves significantly over the best previously known solutions to this problem. We report preliminary experimental results of an implementation of our algorithm. 1 Introduction The problem that we study in this paper is an instance of the assembly partitioning problem [15]: Given a col 3 Work on this paper by L.J. Guibas, D. Halperin and J. C. Latombe has been supported by NSF ARPA Grant IRI9306544, and by a grant from the Stanford Integrated Manufacturing Association (SIMA) Work on this paper by L.J. Guibas and D. Halperin has been also supported by NSF Grant ....

....order to produce a full disassembly step, if one exists. In spite of its limitations, infinitesimal motion is attractive in assembly planning because its analysis translates to handling linear constraints, even when allowing rotation [16] Fore more information on assembly planning see, e.g. 6] [15]. In 1988, in his paper On Planning Assemblies [11] Natarajan conjectured that two hands suffice to assemble any composite comprised of convex polyhedra in 3 space . In a surprising result, Snoeyink and Stolfi [13] have recently been able to disprove this conjecture: they gave an example ....

R.H. Wilson and J.-C. Latombe, Geometric reasoning about mechanical assembly, Journal of Artificial Intelligence, 71 no. 2, 1995, to appear.

....have a null intersection, then S 1 is fully constrained, and the engineer need not be queried. In practice, there can be a very large number of possible subassemblies to test for local freedom. To avoid this inefficiency, our approach generates the locally free subassemblies directly. See [8, 9] for details. 3 A Sufficient Condition: Straight Line Motion A locally free subassembly may require a complex path to separate it fully from the rest of the assembly. To find such a path would require computationally expensive path planning techniques [7] However, for products commonly seen in ....

....can check for the most common types of removal paths, and when these paths are detected, a user query can safely be avoided. One type of simple path consists of a single translation. Efficient methods to find the set of subassemblies removable from an assembly by a single translation are given in [8, 9]. However, many mechanical products include threaded contacts. When a subassembly S 1 has a threaded contact with the rest of the assembly, a helical motion given by the axis of the contact and the pitch of the threads will often remove S 1 . A helical path can be checked exactly by computing the ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2), 1994. 12

....be disassembled [26] However, the inherent combinatorial complexity of trial and error restricts its applicability to very simple products and disassembly sequences where a single part is removed at each step. The non directional blocking graph (NDBG) was proposed to avoid this combinatorial trap [63]. It is a subdivision of the space of allowable motions (e.g. translations) into a finite number of cells such that within each cell the set of blocking relations between all pairs of parts remains fixed. The NDBG is precomputed and then queried to generate assembly sequences. This approach was ....

Wilson, R.H. and Latombe, J.C. 1995. Geometric Reasoning about Mechanical Assembly. Artificial Intelligence, 71:371-396.

....tolerancing [33, 36] As of today, we have only implemented the first procedure, for polygonal assemblies. Section 2 describes the assembly description language accepted by our algorithms. Section 3 gives technical background for the rest of the paper. It summarizes results previously reported in [41, 42], including the concept of the non directional blocking graph (ndbg) of a nominal product, an algorithm to compute ndbgs, and a procedure to generate assembly sequences from an ndbg. Section 4 develops the concept of a strong ndbg for products made of toleranced parts; this ndbg represents all ....

....the region that will be swept by S 2 , and checking that this region does not intersect S 1 . But the number of candidate partitions is exponential in the number of parts in S, while the number of feasible partitions is usually much smaller. The ndbg was introduced to avoid this combinatorial trap [41, 42]. The idea is to precompute a structure, the ndbg, that represents all blocking interferences among the parts in A, and to query this structure to generate one, several, or all disassembly sequences. Consider two parts P i and P j in their relative position in A. Ignore all other parts. The ....

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Wilson, R.H. and Latombe, J.C., Geometric Reasoning About Mechanical Assembly, Artificial Intelligence, 71(2), 371-396, 1994.

.... incorporated heuristics, for example, to drastically reduce the number of separating motions considered by the planner at each partitioning step [9, 21] Some were quite general and hence limited to assemblies with small part count [3] The ndbg was introduced to avoid this combinatorial trap [42, 45]. Arkin, Connelly, and Mitchell [2] use the concept of a monotone path among obstacles to derive a polynomial time algorithm for partitioning an assembly of polygons in the plane with a one step translation. Their algorithm for this special case is more efficient than a straightforward application ....

....these were part of experimental assembly planning systems, while others were stand alone implementations. In this section we give brief descriptions and pointers to those implementations and corresponding experiments. The ndbg was initially implemented in the assembly planner GRASP, described in [42, 45]. GRASP implemented an infinitesimal translation ndbg in 3 D for polyhedral parts. Its implementation was simple but inefficient: it created and analyzed a dbg for the direction of translation given by the intersection of every pair of contact planes in the target assembly. This was supplemented ....

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

....not. Past work has shown that when a disassembly motion may consist of any number of translations, the partitioning problem (and thus sequencing itself) is NP complete [12] On the other hand, polynomial time partitioning is possible when the motions are limited to single translations to infinity [2, 22]. This paper generalizes the non directional blocking graph (or NDBG) of [22] to an intermediate case: motions consisting of a small number of translations. We consider the following problem: given a planar assembly of simple polygons, identify a subassembly that can be removed as a rigid object ....

.... of translations, the partitioning problem (and thus sequencing itself) is NP complete [12] On the other hand, polynomial time partitioning is possible when the motions are limited to single translations to infinity [2, 22] This paper generalizes the non directional blocking graph (or NDBG) of [22] to an intermediate case: motions consisting of a small number of translations. We consider the following problem: given a planar assembly of simple polygons, identify a subassembly that can be removed as a rigid object by a motion consisting of a finite translation followed by a translation to ....

[Article contains additional citation context not shown here]

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

....assembly while (b) is not. partitioning problem (and thus sequencing itself) is NP complete [7] On the other hand, polynomialtime partitioning is possible when the motions are limited to single translations to infinity: Arkin et al. 1] present an algorithm for planar assemblies of polygons, and [12, 13] consider assemblies of polyhedra. This paper generalizes the non directional blocking graph (or NDBG) of [13] to motions consisting of multiple translations. We consider the following problem: given a planar assembly of simple polygons, identify a subassembly that can be removed as a rigid object ....

....polynomialtime partitioning is possible when the motions are limited to single translations to infinity: Arkin et al. 1] present an algorithm for planar assemblies of polygons, and [12, 13] consider assemblies of polyhedra. This paper generalizes the non directional blocking graph (or NDBG) of [13] to motions consisting of multiple translations. We consider the following problem: given a planar assembly of simple polygons, identify a subassembly that can be removed as a rigid object by a motion consisting of a finite translation followed by a translation to infinity. We present an algorithm ....

[Article contains additional citation context not shown here]

R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2), 1994.

.... incorporated heuristics, for example, to drastically reduce the number of separating motions considered by the planner at each partitioning step [7, 20] Some were quite general and hence limited to assemblies with small part count [3] The ndbg was introduced to avoid this combinatorial trap [39, 43]. Arkin, Connelly, and Mitchell [2] use the concept of a monotone path among obstacles to derive a polynomial time algorithm for partitioning an assembly of polygons in the plane with a one step translation. Their algorithm for this special case is more efficient than a straightforward application ....

....these were part of experimental assembly planning systems, while others were stand alone implementations. In this section we give brief descriptions and pointers to those implementations and corresponding experiments. The ndbg was initially implemented in the assembly planner GRASP, described in [39, 43]. GRASP implemented an infinitesimal translation ndbg in 3 D for polyhedral parts, including the connected subassemblies extension of Subsection 8.1. Its implementation was simple but inefficient. It created and analyzed a dbg for the direction of translation given by the intersection of every ....

[Article contains additional citation context not shown here]

R. H. Wilson and J. C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

....that it is guaranteed to find a solution if one exists) simple, and improves significantly over the best previously known solutions. We report experimental results with an implementation of our algorithm. 1 Introduction In this paper we study an instance of the assembly partitioning problem [16]: Given a collection A of nonoverlapping polyhedral parts, does there exist an in Work on this paper by L.J. Guibas, D. Halperin and J. C. Latombe has been supported by NSF ARPA Grant IRI9306544, and by a grant from the Stanford Integrated Manufacturing Association (SIMA) Work on this paper ....

....such a motion, if one exists. In spite of this shortcoming, infinitesimal motions are attractive in assembly planning because their analysis translates to handling linear constraints, even when allowing rotation (see, e.g. 5] 9] 17] Fore more information on assembly planning see, e.g. 6] [16], 18] In 1988, in his paper On Planning Assemblies [12] Natarajan conjectured that two hands suffice to assemble any composite comprised of convex polyhedra in 3 space . In a surprising result, Snoeyink and Stolfi [14] have recently been able to disprove this conjecture: They gave an example ....

[Article contains additional citation context not shown here]

R.H. Wilson and J.-C. Latombe, Geometric reasoning about mechanical assembly, Journal of Artificial Intelligence, 71 no. 2, 1994, pp. 371--396.

.... of the problem (e.g. monotone sequences, where each operation generates a final subassembly, and two handed sequences, where every operation merges exactly two subassemblies) For many of these restricted classes, polynomial algorithms were designed which find an assembly sequence if one exists [20, 21]. There are also algorithms which can enumerate all possible assembly sequences [4] however there may be exponentially many such sequences for a given product. A logical continuation is to use automated reasoning to find the best assembly sequence under a certain complexity measure. Several ....

....a better assembly sequence [3] Although practical, this technique simply delays the eventual need for better automated reasoning to overcome increasingly large data sets. A more complete discussion on using automated reasoning to evaluate the complexity of assembly sequences is given by [20], where they suggest several complexity measures including the number of hands used, the length of the longest sequence of operations, and the number of degrees of freedom required. They prove decidability for some simple questions such as, can a product be assembled entirely from one direction ....

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R. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(1), 1995.

....for the lack of progress on some dynamic graph problems. Fortunately, many real systems have some form of lookahead available, i.e. the dynamic algorithm is provided with information about future updates. In the Appendix, we detail a problem in industrial robotics assembly planning [18, 28, 29, 30] that requires an efficient dynamic algorithm for strong connectivity, and indicate why lookahead is naturally available in this setting. Also, the problem of dynamic transitive closure arises in numerous database applications (see Yannakakis [31] This is equivalent to maintaining the ....

R.H. Wilson and J-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71 (1994).

....and next reversed. Most existing assembly sequencers can only generate two handed monotone sequences. Such a sequence is computed by partitioning the assembly and, recursively, the obtained subassemblies into two separated subassemblies. The non directional blocking graph (NDBG) is proposed in [WL95] to represent all the blocking relations in an assembly. It is a subdivision of the space of all allowable motions of separation into a finite number of cells such that within each cell the set of blocking relations between all pairs of parts remain fixed. Within each cell this set is represented ....

....recursively with the resulting subassemblies. If all the DBGs that are produced during a partitioning step are strongly connected, the algorithm notifies that the assembly does not admit a two handed monotone assembly sequence with infinite translations. Polynomial time algorithms are proposed in [WL95] to compute and exploit NDBGs for restricted families of motions. In particular, the case of partitioning a polyhedral assembly by a single translation to infinity, is analyzed in detail, and it is shown that partitioning an assembly of m polyhedra with a total of v vertices takes O(m 2 v 4 ....

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R.H. Wilson and J.C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71:371--396, 1995.

....available, i.e. the dynamic algorithm is provided with information about future updates. For instance, a frequently arising problem in industrial robotics, namely assembly planning, requires an efficient dynamic algorithm for strong connectivity in presence of naturally available lookahead [18, 28, 29, 30]. Also, the problem of dynamic transitive closure arises in numerous database applications (see Yannakakis [31] This is equivalent to maintaining the transitive closure of a relation undergoing frequent updates, and it is usually desirable to update the transitive closure only after accumulating ....

R.H. Wilson and J-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71 (1994).

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R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

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R. H. Wilson and J.-C. Latombe, "Geometric reasoning about mechanical assembly," Artif. Intell., vol. 71, no. 2, pp. 371--396, Dec. 1994.

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R. H. Wilson and J.-C. Latombe, "Geometric reasoning about mechanical assembly," AI Journal, vol. 72, pp. 371--396, 1994.

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Wilson, R. H. and Latombe, J., 1994, Geometric reasoning about mechanical assembly. ArtiWcial Intelligence, 71, 371 396.

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Wilson RH, Latombe J. Geometric reasoning about mechanical assembly. Artificial Intelligence 1994;71:371--96.

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Wilson, R. H, and Latombe, J., 1994, "Geometric Reasoning about Mechanical Assembly.," Artificial Intelligence, 71, pp. 371-396.

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Wilson, R., Latombe, J. (1994) "Geometric Reasoning About Mechanical Assembly", Artificial Intelligence, Vol 71 (2), pp. 379-396.

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R. H. Wilson and J.-C. Latombe. Geometric reasoning about mechanical assembly. Artificial Intelligence, 71(2):371--396, 1994.

No context found.

R. Wilson and J.-C. Latombe, "Geometric reasoning about mechanical assembly," Artificial Intelligence 71 (1994) 371--396.

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