On the basis, of the condition for demouldability, two levels of visibility, complete and partial visibility, are defined. The viewing directions from which a surface is completely visible can be represented as a convex region on the unit sphere called the visibility map of the surface. Algorithms are given for dividing a given object into pockets, for which visibility and demouldability can be determined independently, for constructing visibility maps, and for selecting an optimal pair of parting directions for a mould that minimizes the number of cores. An example illustrates the algorithms.
Traditional tolerance analyses such as the worst case methods and the statistical methods are applicable to rigid body assemblies. However, for flexible sheet metal assemblies, the traditional methods are not adequate: the components can deform, changing the dimensions during assembly. This paper evaluates the effects of deformation on component tolerances using linear mechanics. Two basic configurations, assembly in series and assembly in parallel, are investigated using analytical methods. Assembly sequences and multiple joints beyond the basic configurations are further examined using numerical methods (with finite element analysis). These findings constitute a new methodology for the tolerancing of deformable parts.
Exact algorithms for detecting all rotational and involutional symmetries in point sets, polygons and polyhedra are described. The time complexities of the algorithms are shown to be O(n) for polygons and O(nlogn) for two-and three-dimensional point sets. O(n logn) time is also required for general polyhedra, but for polyhedra with connected, planar surface graphs O(n) time canbe achieved. All algorithms are optimal in time complexity, within constants.
The paper surveys the current state of knowledge of techniques for representing, manipulating and analysing dimensioning and tolerancing data in computer-aided design and manufacturing. The use of solid models and variational geometry, and its implications for the successful integration of CAD and CAM, are discussed. The topics explored so far can be grouped into four categories: (a) the representation ot dimensioning and tolerancing (D& T), (b) the synthesis and analysis of D& T, (() tolerance control, and (d) the implications of D& T in CAM. The paper describes in detail the recent work in each group, and concludes with speculation on a general framework k)r future research. dimensioning, toleran(ing, CAI~).'(-AM, ~olid models, variational ~('om('try
Tolerance, representing a permissible variation of a dimension in an engineering drawing, is synthesized by considering assembly stack-up conditions based on manufacturing cost minimization. A random variable and its standard deviation are associated with a dimension and its tolerance. This probabilistic approach makes it possible to perform trade-off between performance and tolerance rather than the worst case analysis as it is commonly practiced. Tolerance (stack-up) analysis, as an inner loop in the overall algorithm for tolerance synthesis, is performed by approximating the volume under the multivariate probability density function constrained by nonlinear stack-up conditions with a convex polytope. This approximation makes use of the notion of reliability index [10] in structural safety. Consequently, the probabilistic optimization problem for tolerance synthesis is simplified into a deterministic nonlinear programming problem. An algorithm is then developed and is proven to converge to the global optimum through an investigation of the monotonic relations among tolerance, the reliability index, and cost. Examples from the implementation of the algorithm are given.
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