Machinery's Handbook, 31st Edition
COMPOUND ANGLES
121
Formulas for Compound Angles
For given angles A and B , find the resultant angle C in plane x - x . Angle B is measured in vertical plane y - y of midsection. Fig. 1 C tan A tan B cos × = Fig. 2 C tan A tan B cos = ------ Fig. 3 (Same formula as for Fig. 2) Fig. 4. In machining a plate to angles A and B , the plate is held at angle C in plane x - x . Angle of rotation R in plane parallel to base (or complement of R ) is for locating plate so that plane x - x is perpendicular to axis of pivot on angle-plate or work-holding vise. R tan C tan = = , Fig. 5. Angle R in horizontal plane parallel to base is angle from plane x - x to side having angle A . R tan A tan B tan = ------ tan C = tan A × cos R = tan B × sin R Compound angle C is angle in plane x - x from base to corner formed by intersection of planes inclined to angles A and B . This formula for C may be used to find cotangent of complement of C 1 , Fig. 6. B tan A tan ------ A tan R cos ------ Fig. 6. Angles A 1 and B 1 are measured in vertical planes of front and side elevations. Plane x - x is located by angle R from center-line or from plane of angle B 1 . R tan
y
y
y
y
y
y
A
A
A
C
C
C
x
x
x
x
B
x
x
B
B
B
B
Fig. 2.
Fig. 3.
Fig. 1.
x
C
B
R
x
A
Fig. 4.
C
x
B
R
x
A
Fig. 5.
x
R
B 1
C 1
A 1 tan B 1 tan = -------
A 1
x
A 1 tan R sin -------
B 1 tan R cos -------
C 1 tan = The resultant angle C 1 would be required in drilling hole for pin. =
Fig. 6.
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