Requicha, A.A.G, Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches, in Solid Modeling by Computers: From Theory to Applications, Pickett, M.S. and Boyse, J.W. (eds.), Plenum Press, New York, 3-22, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for extending informational completeness to parametric solid modeling and for creating an industry wide standard for data exchange of parametric models. To our knowledge, there are no competing proposals. A notion of variational class is prominent in mechanical tolerancing and robustness [29, 36]. Notably, Stewart proposed a definition of variational class in [36] which was later used in study of polyhedral perturbations that preserve topological form in [3] The assumptions of continuity and continuous deformation are also mentioned informally in the naming techniques and discussion of ....

A. A. G. Requicha. Representation of tolerances in solid modeling: Issues and alternative approaches. In Solid Modeling by Computers, Pickett, M.S and Boyse J.W (Eds). Plenum Publishing Corp, USA, 1984.

....offsetting which is the sweep of a constant radius circular disc along a 2D curve trajectory. The offset curves can be used for automatic generation of NC machining tool paths in CAD CAM. There are also various other applications of offset curves in modeling geometric uncertainty tolerancing [33, 34], solid smoothing, filleting, and blending [36, 37] etc. However, even for low degree algebraic curves, the corresponding offset curves have relatively high algebraic degrees. For example, the offset curve of parabola has degree 6 [7] Since high degree algebraic curves are not easy to compute ....

Requicha, A., "Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches, " in Solid Modeling by Computers: From Theory to Applications , edited by M. Pickett and J. Boyse, Plenum Press, New York, pp. 3--22, 1984.

....of the axis of a hole. Researchers found that such theories did not allow consistent geometries or topologies to be maintained. Other researchers struggled to find consistent theories that did not rely on a plethora of special cases. Unfortunately, these theories, of which that of Requicha [14] is perhaps the most widely cited example, did not produce interpretations that corresponded to practical applications of tolerances [15] A recent proposal by Jayaraman and Srinivasan [16,17] to address this issue is to base tolerance semantics on the notion of virtual boundaries. A virtual ....

Requicha, A., "Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches," in Solid Modelling by Computers: From Theory to Applications, pp.

....have toleranced geometry. This work has been motivated by the fact that for many products, tolerances have crucial effect on assembly sequences and manufacturing costs. Part tolerancing addresses the fact that manufacturing processes are inherently imprecise and produce parts of variable shapes [34, 38]. A large body of work has been devoted to the development of tolerance languages (e.g. Y14.5 [1, 39] providing designers with symbolic means to specify acceptable variations. One important goal is to guarantee part interchangeability in an assembly product [38] given any set of parts ....

Requicha, A.A.G, Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches, in Solid Modeling by Computers: From Theory to Applications, Pickett, M.S. and Boyse, J.W. (eds.), Plenum Press, New York, 3-22, 1984.

....and tolerancing for designing and manufacturing components of mechanical products. The main intended use was for manufacturing and inspection. If specified correctly by the designers, tolerances can also guarantee the assemblability between two parts with multiple mating features. Requicha [1,8] proposed tolerance zones, which are regions constructed by offsetting nominal boundaries of features. The objective was to formalize and generalize the tolerance practice and to establish a suitable bases for incorporating tolerances to solid modeling systems [9] Whitney and Gilbert [2] proposed ....

A. A. G. Requicha, "Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches", in Solid Modeling by Computers: from Theory to Applications, J. W. Boyse and M. S. Pickett, Eds. New York: Plenum, pp. 3-22, 1984.

....assembling the parts given the dimension specification and the tolerance specifications, as well as the mating constraint including the positions of mating features in an assembly, clearances of mating features, and the functionality of parts. 1. 1 Related Work For geometry modelling, Requicha [1, 2] proposed the concept of tolerance zones. The objective of the proposed tolerance theory was to formalize and generalize the tolerance practice. For the analysis, Whitney and Gilbert [3] proposed transform matrix representation for tolerances in ANSI standard [4] For the functionality analysis, ....

A. A. G. Requicha. Representation of tolerances in solid modeling: Issues and alternative approaches. in Solid Modeling by Computers: from Theory to Applications, J. W. Boyse and M. S. Pickett, Eds. New York: Plenum:3--22, 1984.

....are rigid such that they do not deform nor have subparts that translate or rotate. 2) There exists a clearance between two mating features. 3) The nominal parts will always assemble successfully. 4) Tolerances are assumed to have a Gaussian distribution. 2 Related Work and Background Requicha [3, 4] proposed to represent tolerances using tolerance zones which are regions constructed by offsetting nominal boundaries of features. The objective of the proposed tolerance theory was to formalize and generalize the tolerance practice and to establish a suitable bases for incorporating tolerances ....

A. A. G. Requicha. Representation of tolerances in solid modeling: Issues and alternative approaches. in Solid Modeling by Computers: from Theory to Applications, J. W. Boyse and M. S. Pickett, Eds. New York: Plenum:3--22, 1984.

....a theoretical model of tolerancing, or tolerance representation scheme, that is in accordance with the international standards. An early example of previous work in order to come to a mathematically correct model for tolerancing is the solids offset approach by Requicha [Requicha 83] extended in [Requicha 84, 86] In this approach, nominal surfaces are given a pair of offset surfaces to determine the tolerance zones. This approach differs from the tolerancing standards [Farmer 86] Because the individual pairs of offset surfaces are combined to obtain a composite tolerance zone of the entire solid, ....

Requicha A.A.G., Representation of tolerances in solid modeling: issues and alternative approaches, in: Solid modeling by computers, from theory to applications, eds. Picket M.S., Boyse J.W., Plenum press, 1984.

....for choosing a particular value for the tolerance zone (tolerance assignment) is not addressed; in other words, performance is not directly addressed. Hence, this theory is found wanting with respect to the two requirements above. Requicha mentions these issues in the development of the theory [138], but focuses on the representation problem. This implies the assumption that the value of the tolerance zone given to the designer is correct. A more fundamental question arises from the first requirement, i.e. are the manufacturing variations adequately captured in a tolerance zone The ....

A. A. Requicha. Representation of tolerances in solid modeling: Issues and alternative approaches. In J. W. Boyse, editor, Solid Modeling by Computers: from Theory to Applications, pages 3--22. Plenum Press, New York, 1984.

....verification, the emphasis here is upon the inclusion of topological considerations as essential for design optimization. 2 Introduction: Topological Invariance The desirability of topological invariance during iterative redesign was initially expressed relative to tolerance modeling [20, 21]. There, the treatment was largely informal, but mathematically rigorous foundations for preservation of topological form have subsequently been proposed [6, 7] Consistent with these cited works, the definition given here for topological tolerance is analogous to the typical use of dimensional ....

Requicha, A. A. G., Representation of tolerances in solid modeling: issues and alternative approaches, in Solid Modeling by Computers, eds., Pickett, M. S. and Boyse, J. W., Plenum, USA, 1984.

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Requicha, A.A.G, Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches, in Solid Modeling by Computers: From Theory to Applications, Pickett, M.S. and Boyse, J.W. (eds.), Plenum Press, New York, 3-22, 1984.

No context found.

Requicha, A.A.G. 1984. Representation of tolerances in solid modeling: Issues and alternative approaches. In Solid Modeling by Computers: From Theory to Applications, ed. M. S. Pickett and J. W. Boyse, 3--22. New York: Plenum.

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