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Unformatted text preview: ing hypersections in Fig. 2, those that contain the coordinate M'. Presuming the x-axis in Fig. 1(b) to be aligned parallel to Datum B, the feature control frame 0.05 B on parallelism limits to 0.05 mm the projection in the y-direction of a length j along the axis; i.e. coordinate M' is limited to the range –0.05 ≤ M' ≤ 0.05 mm. The truncated hypersection for Fig 2(b) is shown in Fig 5. When the hypersections in Figs 2(c) and (d) are truncated along the M' axis, the resulting solids are congruent to the one shown in Fig. 4(a), although the placement of coordinate axes would be different. CONCLUSION Tolerance-Maps were created for both a perpendicularity tolerance and a parallelism tolerance, relative to a datum plane, each applied to an axis located with a position tolerance. Using areal coordinates and traditional geometry of lines, the T-Maps were created as 4-D objects and visualized using 3-D hypersections. The T-Map for straightness of an axis was developed as an internal subset to the T-Map for position. This concept led Tole...
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