A knowledge of arc relationships is required when working with curves in AutoCAD design and programming.
Definitions[]
r=radius
delta=included angle
tan(angle)=sin(angle)/cos(angle)
Units[]
delta in radians
- =delta in degrees*pi/180
- =delta in degrees/57.2957786666 approx.
delta in degrees
- =delta in radians*180/pi
- =delta in radians*57.2957786666 approx.
Relationships[]
For all these relationships, angles are in radians. Angle 2 is the angle of triangle 123 at Point 2
Arc length=r*delta
Chord=r*tan(delta/2)
Bulge=tan(delta/4)
- =b/(chord/2)
- =2b/chord
Tangent
- =r*tan(delta/2)
- =r*sin(delta/2)/cos(delta/2)
Delta
- =4*arctan(bulge)
R
- =chord/(2*sin(delta/2)))
- =arc length/delta
Angle 2 (even when point 2 is not at midpoint of arc)
- =(2*pi-delta)/2
- =pi-(angle1+angle3)
- =arcsin(chord/(2*R))