The assemblability, which is the probability of successfully assembling the product parts, is directly related to the product cost. Especially, we consider the assembly failures due to tolerances. Because clearances provide the adjustability to part poses in an assembly, the assemblability analysis must be analyzed not only in terms of tolerances but also clearances. In this paper, we propose an analytic approach to the assemblability analysis. Represented by ellipsoids in a deviation space, the propagations of tolerances and clearances are calculated using Jacobian and sweep operations. The simulation results are given using a 2D assembly. The expected contribution of this paper is that the proposed method allows to compute the assemblability of a product in real time.

We present an augmented space method to solve the assemblability of products where tolerances may prevent parts assembling successfully. The accumulated tolerances of two serial chains of the parts are modeled by a hyper-ellipsoid in an augmented space. By the same token, the accumulated nominal clearances of two serial chains are modeled by a hyper-ellipsoid. Complete algorithms for solving the assemblability, tolerance, and clearance of parallel chains in the augmented space are described. This augmented space method gives a great computational advantage over simulation based methods, which is a necessary requirement for the real time assemblability analysis. Simulation results are given.

We present an approach for evaluating the assemblability of a product based on tolerances and adjustable displacements. An adjustable displacement is a functionally permitted free space between two mating features, which can be used for compensating tolerances. The assemblability of a product is computed in term of a multi chain by incrementally solving the parallel chains. We consider both the functionality and assembly sequence constraint in the evaluation. The result of the computation is a statistical measure of the product assemblability which can be used by the designer to evaluate and to optimize the tolerance allocation. In addition, this measure can be used for evaluating assembly sequences. The algorithms and simulation results are given.

An assembly task, whether robotic or manual, may involve adjusting the positions of already assembled parts when a new part is assembled, due to tolerance and position uncertainties of the parts. Such an adjusting operation can increase the cost of the product because of the adjusting time, fixturing costs, additional operations, etc. In this paper, a statistical approach to evaluate the cost of assembly is proposed. The cost is measured according to the number of objects that must be moved in order to successfully assemble the product. The approach uses a statistical analysis of the accumulated tolerances, the local clearances, and the possible adjustable zones due to clearances between the already assembled parts, to calculate the minimum number of objects that must be adjusted to complete the assembly. Special attention is given to the assembly of parallel chains. The complete procedure and simulation results are given.

In this paper, we present statistical tolerance and clearance analysis for the assembly. Tolerances work against the assemblability of a product since they can propagate and accumulate in the product, making it more difficult or impossible to assemble. Clearances work for the assemblability since they can be used to compensate for tolerances. The poses of parts in an assemble may be adjusted within the permitted clearances to assemble the parts. Monte-Carlo method is used in the analysis, with Gaussian distribution, Gaussian-Sigmoid distribution, and Chi-Square error reduction scheme to approximate tolerances and clearances. Then, algorithms to compute the propagation of tolerances and clearances are proposed. Our proposed work is expected to make the following contributions: 1) to help the designers to evaluate products for assemblability, 2) to provide a new perspective to tolerance problems, and 3) to provide a tolerance analysis tool which can be incorporated into a CAD or solid modeling system.

Fixtures are devices used in manufacturing to immobilize a part far operations such as assembly, inspection or machining. Modular fixtures are configurations of standard components. The goal of a automatic modular fixture design is to find algorithms to determine a set of fixturing contact points automatically, given a set of modular components and the fixturing requirements. This paper considers the problem of generating valid assembly sequences for a given modular future configuration. This is called assembly planning for modular fixtures. Because the application domain is known, we can devise an efficient assembly planning system taking advantage of the characteristics of the fixture domain. In this paper, we propose a fastener-based approach which considers the functionality of fasteners (to hold the fixture components together) to achieve both the efficiency in assembly planning and the stability of the generated assembly sequences. We also describe an accessibility measure that can be used to select preferred assembly sequences. This work complements automatic fixture design such that complete automation can be achieved from the design of a fixture to its assembly, which can be performed manually or with the aid of robots.

The specification of tolerances is an integral part of product design since tolerances directly affect the assemblability, as well as the functionality, manufacturability, and cost-effectiveness of the product. However, there has been little research on the assemblability evaluation based on tolerance propagation which can play an important role in assembly planning. Assembly planners in the past have assumed nominal dimensions for product components for generating the feasible assembly sequences. These sequences, however, may not be assemblable in practice due to propagations and accumulations of tolerances. In this paper, we present a new approach to assemblability evaluation based on tolerance propagation. For the assemblability evaluation, we introduce an important concept of clearance. Clearance represents the possible free space between two mating features. In the assemblability evaluation, clearances are used to compensate for tolerances.

In this paper we present a statistical approach to assemblability evaluation based on tolerance and clearance propagations. Tolerance affect assemblability of an assembly sequence, however, clearance can compensate for tolerance. Assembly planners in the past have assumed nominal dimensions for product components for generating feasible assembly sequences. These sequences, however, may not be assemblable in practice due to propagations and accumulations of tolerances. With this concept of clearance, approaches to compute statistical tolerance and clearance propagations for serial, parallel, and multi-loop chains are proposed. The proposed method can be a valuable tool for CAD/CAM since early detection of assembly problems can significantly reduce the product cost.

Force-based reasoning, for identifying a cluster of parts that can be decomposed naturally by the applied force, plays an important role in selecting feasible subassemblies and analyzing subassembly stability in assembly planning. This is because force-based reasoning provides a new set of constraints which are distinctive from those from geometric reasoning. Such constraints not only enhance the planning efficiency but also allows stability analysis in terms of subassembly deformation due to the mating forces. Specifically, force-based reasoning can be applied during subassembly identification to eliminate unstable subassemblies that are deformable during the mating operation.