Machinery's Handbook, 31st Edition
Angles and Tapers
697
Accurate Measurement of Angles and Tapers When great accuracy is required in the measurement of angles, or when originating tapers, disks are commonly used. The principle of the disk method of taper measurement is that if two disks of unequal diameters are placed either in contact or a certain distance apart, lines tangent to their peripheries will represent an angle or taper, the degree of which depends upon the diameters of the two disks and the distance between them.
A
B 1
C
B
α
A 1
The gage shown in the accompanying illustration, which is a form commonly used for originating tapers or measuring angles accurately, is set by means of disks. This gage con sists of two adjustable straight edges A and A 1 , which are in contact with disks B and B 1 . The angle α or the taper between the straight edges depends, of course, upon the diameters of the disks and the center distance C , and, as these three dimensions can be measured accurately, it is possible to set the gage to a given angle within very close limits. Moreover, if a record of the three dimensions is kept, the exact setting of the gage can be reproduced quickly at any time. The following rules may be used for adjusting a gage of this type and cover all problems likely to arise in practice. Disks are also occasionally used for the set ting of parts in angular positions when they are to be machined accurately to a given angle: the rules are applicable to these conditions also. Measuring Dovetail Slides.— Dovetail slides that must be machined accurately to a given width are commonly gaged by using pieces of cylindrical rod or wire and measuring as indicated by the dimensions x and y of the accompanying illustrations. x y
e
h
D
D
c
a
b
The rod or wire used should be small enough so that the point of contact e is somewhat below the corner or edge of the dovetail. To obtain dimension x for measuring male dovetails, add 1 to the cotangent of one-half the dovetail angle α, multiply by diameter D of the rods used, and add the product to dimension α. cot cot x D a c h 1 k To obtain dimension y for measuring a female dovetail, add 1 to the cotangent of one- half the dovetail angle α, multiply by diameter D of the rod used, and subtract the result from dimension b . Expressing these rules as formulas: cot y b D 1 2 1 α = − + a k 2 1 # α α = + a + =
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