Page 561 - Cam Design Handbook

THBAP 9/19/03 7:29 PM Page 549

BASIC CONTOURS 549

M B O Q P
Base circle radius, a
g

R
F ¢
D
F ≤

N
FIGURE A.7. Construction of the logarithmic spiral.

c) From point O, swing arc of radius BF intersecting arc of radius DF from point D.
d) This gives one point F¢ on the curve; other points are found in a similar manner uti-
lizing the same centers O and D.

It may be noted that portion DQ of the curve is subject to greater error than portion
DR. Caution and accuracy are suggested for this critical range.

A.5 INVOLUTE OF A CIRCLE

This is a curve generated by the end of a string unwinding from an involute base circle
of radius a (Fig. A.8).
The equation of the involute is
2 12 2 12
È r ˘ È r ˘
Ê ˆ
Ê ˆ
q = Í -1 ˙ - tan -1 Í -1 ˙ .
Ë ¯
Ë ¯
Î a ˚ Î a ˚
g
q
Radius of
curvature a

FIGURE A.8. Involute of a circle.

Construction:
Given the base circle having radius a in Fig. A.8,