This paper presents a comparison of degree of freedom (DOF) based math models, viz., tolerance-maps, deviation domain, and TTRS, which have shown most potential for retrofitting the nuances of the ASME/ISO tolerance standards. Tolerances specify allowable uncertainty in dimensions and geometry of manufactured products. Due to these characteristics and application of tolerances, it is necessary to create a math model of tolerances in order to build a computer application to assist a designer in performing full 3D tolerance analysis. Many of the current efforts in modeling tolerances are lacking, as they either do not completely model all the aspects of the ASME/ISO tolerance standards or are lacking the requisite full 3-D tolerance analysis. Some tolerance math models were developed to suit CAD applications used by the designers while others were developed to retrofit the ASME/ISO tolerance standard. Three math models developed to retrofit the ASME/ISO standard, tolerance-maps, deviation domain, and TTRS are the main focus of this paper. Basic concepts of these math models are summarized in this paper, followed by their advantages and future issues. Although these three math models represent all aspects of the ASME/ISO tolerance standard, they are still lacking in one or two minor aspects.

. Tolerance analysis and synthesis by means of deviation domains, axi-symmetric cases. J Davidson. Models for computer aided tolerancing in design and manufacturing, springer, pp. 84-94, 2007, engineering, <10.1007/1-4020-5438-6_10>.

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The periodical D-band pattern is generally considered a unique ultrastructural feature shared by all fibril-forming collagens, which correlates with the intrafibril, paracrystalline array of tropocollagen monomers. Distinct band patterns have been reported, however, for collagen stained long-spacing (SLS) crystallites of genetic types I, II, and III. Moreover, D-band patterns of negatively stained, native type II collagen fibrils were found to be not identical to those of type I in our previous research. Because of (a) these distinctive features, (b) tropocollagen heterotrimeric conditions (type I) vs homotrimeric conditions (type II), and (c) different lengths and poor homology between extrahelical telopeptides, the molecular array or telopeptide conformation within the extensively studied type I collagen fibrils could be not the same as those in the very much less intensively studied type II collagen fibrils. In this investigation, a distinctive positive-staining D-band pattern was found for type II collagen fibrils obtained from human cartilages. A fibril model was developed by analyzing actual D-band patterns, and matching them against simulated patterns based on the primary structure of extrahelical and helical domains in human type II tropocollagen. In particular, a more prominent b(1) band was apparent in native type II collagen fibrils than in type I. This distinctive feature was also observed for native-type collagen fibrils reconstituted from purified type II collagen, i.e., free from associated minor type XI collagen. On modeling possible monomer arrays, the best fit between microdensitograms and simulation traces was found for 234 amino acid staggering, as is also the case for type I collagen fibrils. On comparing this model with an analogous one for type I collagen fibrils, there was a higher intraband distribution of charged residues for band b(1), consistent with the higher electrondensity observed for this band in type II collagen fibrils. N- and C-telopeptide displacement in the model corresponded to D-locations of a c(2) subband, which we named c(2.0), and band a(3), respectively. In simulation profiles, c(2.0) -like and a(3) -like peaks mimicked the corresponding peaks in microdensitograms when molecular reversals were adopted at positions 10N-12N, 12C-14C, and 17C-19C for N- and C-telopeptides. Hydrophobic interactions and algorithmic predictions of protein secondary structure, according to Chou and Fasman and Rost and Sander criteria, were consistent with these conformational models, and suggest that an additional molecular reversal may occur at positions 3N-5N. These telopeptide "S-fold" conformations, interpreted as axial projections of tridimensional conformation, may represent starting points for further investigation into the still unresolved tridimensional conformation of telopeptides in monomers arrayed within type II collagen fibrils.