G asme 1994 of diameter t and length j within which

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Unformatted text preview: he quadratic identity to be met with only a residue of order [t 4], yet the terms added together are of order [t2]. Since position tolerance t is two or more orders of magnitude smaller than any dimension on a part, the residue is four or more orders of magnitude smaller than the largest term in the sum.) Equation (1) can be expanded to 0 0 t / l 0 λ1 λ1 0 L λ 0 M 0 0 0 t / l λ 2 2 N = [ X ] λ 3 = 1 (2) 1 1 1 1 λ3 0 t/2 0 0 λ 4 λ 4 0 P λ 5 0 − t / 2 0 Q 0 0 λ 5 2 Vector (L,M,N) contains the direction cosines of the line, and vector (P,Q,R) is the moment that a unit force along the line would produce about the origin. Consequently, the six Plücker coordinates are constrained by the quadratic identity LP + MQ + NR = 0. Tolerance-Maps for Straightness and Orientation 49 L' $4 $4 L' Q Q $6 $1 $2 $3 $7 $9 $1 $6 P $2 $5 M' $8 (a) (b) $8 M' $5 M' $5 Q L' $7 $6 $1 $3 $2 $7 $4 $1 $3 P $9 (d) $8 P $9 (c) Figure 2. Four three-dimensional hypersections of the T-Map and its basis 4-simplex for the tolerance-zone in Fig. 1(b) (for posi...
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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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