We present design principles for creating effective assembly instructions and a system that is based on these principles. The principles are drawn from cognitive psychology research which investigated people’s conceptual models of assembly and effective methods to visually communicate assembly information. Our system is inspired by earlier work in robotics on assembly planning and in visualization on automated presentation design. Although other systems have considered presentation and planning independently, we believe it is necessary to address the two problems simultaneously in order to create effective assembly instructions. We describe the algorithmic techniques used to produce assembly instructions given object geometry, orientation, and optional grouping and ordering constraints on the object’s parts. Our results demonstrate that it is possible to produce aesthetically pleasing and easy to follow instructions for many everyday objects.

Assembly planning is the problem of finding a sequence of motions to assemble a product from its parts. We present a general framework for finding assembly motions based on the concept of motion space. Assembly motions are parameterized such that each point in motion space represents a mating motion that is independent of the moving part set. For each motion we derive blocking relations that explicitly state which parts collide with other parts; each subassembly (rigid subset of parts) that does not collide with the rest of the assembly can easily be derived from the blocking relations. Motion space is partitioned into an arrangement of cells such that the blocking relations are fixed within each cell. In the first part of the paper we give background material, present the motion space approach and describe applications of the approach to assembly motions of several useful types, including one-step translations, multi-step translations, and infinitesimal rigid motions. Several efficien...

The goal of assembly sequencing is to plan a feasible series of operations to construct a product from its individual parts. Previous research has investigated assembly sequencing under the assumption that parts have nominal geometry. This paper considers the case where parts have toleranced geometry. Its main contribution is an efficient procedure that decides if a product admits an assembly sequence with infinite translations (i.e., translations that can be extended arbitrarily far along a fixed direction) that is feasible for all possible instances of the components within the specified tolerances. If the product admits one such sequence, the procedure can also generate it. For the cases where there exists no such assembly sequence, another procedure is proposed which generates assembly sequences that are feasible only for some values of the toleranced dimensions. If this procedure produces no such sequence, then no instance of the product is assemblable. These two proced...

Our work examines various complexity measures for two-handed assembly sequences. For many products there exists an exponentially large set of valid sequences, and a natural goal is to use automated systems to select wisely from the choices. Since assembly sequencing is a preprocessing phase for a long and expensive manufacturing process, any work towards ndinga\better" assembly sequence isofgreat value when it comes time to assemble the physical product in mass quantities. We take a step in this direction by introducing a formal framework for studying the optimization of several complexity measures. This framework focuses on the combinatorial aspect of the family of valid assembly sequences, while temporarily separating out the speci c geometric assumptions inherent to the problem. With an exponential number of possibilities, nding the true optimal cost solution is non-trivial. In fact in the most general case, our results show that even nding an approximate solution is hard. Furthermore, we can show several hardness results, even in simple geometric settings. Future work is directed towards using this model to study how the original geometric assumptions can be reintroduced toprove stronger approximation results. 1

In this paper, we present a software system which can automatically determine how to assemble a product from its parts, given only a geometric description of the assembly. Incorporated into a larger CAD tool, this system, the Stanford Assembly Analysis Tool (STAAT), could thus provide immediate feedback to a team of product designers about the complexity of assembling the product being designed. This would be particularly useful in complex assemblies where each designer may not be fully aware of the impact of his design changes on the assemblability of the product as a whole. STAAT’s underlying data structure is an efficient version of the non-directional blocking graph (NDBG), a compact representation of the blocking relationships in an assembly. STAAT implements several techniques using this structure, under a unified approach in which the same software “machinery ” can analyze the product under different assembly constraints. In initial experiments conducted on relatively small polyhedral assemblies of 20 to 40 parts and 500 to 1500 faces, using one-step translational motions, STAAT generated assembly sequences much more quickly than did previous NDBG-based systems. We are working now on extending both these results and the underlying theory to more sophisticated cases.

Consider the following decision problem. Given a collection of non- overlapping (but possibly touching) polygons in the plane, is there a proper connected subcollection of it that can be separated from its complement moving as a rigid body, without disturbing the other parts of the collection, and such that the complement is also connected? We show that this decision problem is NP-complete. This had been known to be true without the connectedness requirement, and also with this requirement but in three-dimensional space.

Let S be a collection of n rigid bodies in 3-space, and let D be a set of k directions in 3-space, where k is a small constant. A k-directional assembly sequence for S, with respect to D, is a linear ordering hs1 ; : : : ; sni of the bodies in S, such that each s i can be moved to infinity by translating it in one of the directions of D and without intersecting any s j , for j ? i. We present an algorithm that computes a k-directional assembly sequence, or decides that no such sequence exists, for a set of polyhedra. The algorithm runs in O(km 4=3+" ) time, where m is the total number of vertices of the polyhedra. We also give an algorithm for `k-directional' rotational motions.

Abstract. We consider the problem of removing a given disk from a collection of unit disks in the plane. At each step, we allow a disk to be removed by a collision-free translation to infinity, and the goal is to access a given disk using as few steps as possible. This Disks problem is a version of a common task in assembly sequencing, namely removing a given part from a fully assembled product. Recently there has been a focus on optimizing assembly sequences over various cost measures, however with very limited algorithmic success. We explain this lack of success, proving strong inapproximability results in this simple geometric setting. Namely, we show that approximating the number of steps required to within a factor of 2 log1−γ n for any γ>0 is quasi-NP-hard. This provides the first inapproximability results for assembly sequencing, realized in a geometric setting. As a stepping stone, we study the approximability of scheduling with and/or precedence constraints. The Disks problem can be formulated

We consider the following problem that arises in assembly planning: given an assembly, identify a subassembly that can be removed as a rigid object without disturbing the rest of the assembly. This is the assembly partitioning problem. Specifically, we consider planar assemblies of simple polygons and subassembly removal paths consisting of a single finite translation followed by a translation to infinity. Such paths are typical of the capabilities of simple actuators in fixed automation and other high-volume assembly machines. We present a polynomial-time algorithm to identify such a subassembly and removal path. We discuss extending the algorithm to 3D, other types of motions typical in non-robotic automated assembly, and motions consisting of more than two translations. 1 Introduction Fixed automation or special-purpose assembly machines can achieve very high throughput, often down to cycle times of one product per second for synchronous assembly machines and similar systems, and ...

The problem of deciding whether 2- or 3-dimensional objects can be separated by a sequence of arbitrary translational motions is known to have exponential lower bounds. However, under certain restrictions on the type of motions, polynomial time bounds have been shown. An example is finding a subset of the parts that is removable by a single translation. In this case,