Page 557 - Cam Design Handbook

THBAP 9/19/03 7:29 PM Page 545

APPENDIX A

BASIC CONTOURS

A.1 ELLIPSE 545 A.4 LOGARITHMIC SPIRAL 548
A.2 PARABOLA 545 A.5 INVOLUTE OF A CIRCLE 549
A.3 HYPERBOLA 546

A.1 ELLIPSE

An ellipse is a curve generated by a point moving so that the sum of the distances from
the two fixed points (F 1 and F 2) called foci is a constant. The basic equation for the ellipse
is
X 2 Y 2
+ = 1 (Eq. A.1)
a 2 b 2

where X = value of the curve in one direction
Y = value of the curve in other direction
1
a = / 2 major axis
1
b = / 2 minor axis
We note that the foci of the ellipse F 1 and F 2 are a distance a from the ends of the
minor axis. Also the major axis equals 2a in length. For construction of the ellipse the
reader is referred to Sec. 2.3.

Y

a a b

X
F 1 F 2

a
FIGURE A.1. Ellipse.

A.2 PARABOLA

A parabola is a curve generated by a point moving so that its distance from a fixed point
F, called the focus, is always equal to its distance from a fixed straight line called the
directrix. In Fig. A.2, the distance X, Y, and e are shown to any point P on the curve. AB
is the directrix. Since from the definition X = e, we have the basic equation
2
Y = CX

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