Machinery's Handbook, 31st Edition
704 Measurement OVER PINS AND Rolls Referring to Fig. 3a for the concave gage, if L and D are known, cb can be found, and if H and D are known, ce can be found. With cb and ce known, ab can be found by means of a diagram as shown in Fig. 3c. In diagram Fig. 3c, cb and ce are shown at right angles as in Fig. 3a. A line is drawn con necting points b and e, and line ce is extended to the right. A line is now drawn from point b perpendicular to be and intersecting the extension of ce at point f . A semicircle can now be drawn through points b , e , and f with point a as the center. Triangles bce and bcf are similar and have a common side. Thus ce : bc :: bc : cf . With ce and bc known, cf can be found from this proportion and, hence, ef, which is the diameter of the semicircle and radius ab . Then R = ab + D /2. L a
e
R
b H
c
D
c
D
b
R
e
L
a
Fig. 3a.
Fig. 3b.
b
e
f
c
a
Fig. 3c. The procedure for the convex gage is similar. The distances cb and ce are readily found, and from these two distances ab is computed on the basis of similar triangles as before. Radius R is then readily found. The derived formulas for concave and convex gages are as follows: Formulas: R H D L D H 8 2 2 = − − + ^ ^ h h (Concave gage Fig. 3a) R D L D 8 2 = − ^ h (Convex gage Fig. 3b) For example: For Fig. 3a, let L = 17.8, D = 3.20, and H = 5.72, then . . . . . . . . . . . . R R 8 572 320 178 320 2 572 8 252 1460 286 2016 213 16 2 86 13 43 2 2 # = − − + = + = + = ^ ^ ^ h h h
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online