A the central hyperplane 5 0 b the hyperplane 3 0

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Unformatted text preview: ide, et al., 2003]); the result is the fourdimensional T-Map that is shown in Fig. 2 with four 3-D hypersections. Equation (1) implies a one-to-one relationship between the line-segments in the tolerance-zone of Fig. 1(b) and the points in the 4D space that is described with areal coordinates. Therefore, it can be used to identify any point in the T-Map of Fig. 2 by interpreting $1, …,$5 to represent the five basis-points chosen in Fig. 2. Correspondingly, it can be used to identify any line in the tolerance-zone of Fig. 1(b) by assigning $1, …,$5 to represent the five basis-lines chosen in Fig. 1(b), a suggestion that clearly is not valid in general because linear combinations of two lines yield screws, not lines. However, Eq (1) may be used for the lines in a tolerance-zone because every one of these lines is rotated only slightly from the theoretical orientation of the feature axis. This assertion was proved in [Davidson & Shah, 2002]. (The constraint of slight rotations causes t...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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