20 Jun
2024
20 Jun
'24
10:41 p.m.
2/24 it said an involute curve is like unwinding a spool of thread …
so if unwinding thread, basically the length of your line is equal to the arc length it was unwound from.
we could describe that as a function of the angle of unwinding. for each point on the circumference, there’d be an associated line length.
- (point on circumference) + (vector of tangent) * arclength
function of angle
r = radius of spool t = time/theta
x(t) = r * (cos(t) + t * sin(t))
y(t) = r * (sin(t) - t * cos(t)) p(t) = r * (exp(i t) - i t * exp(i t))
parametric plot (cos(t) + t * sin(t)), (sin(t) - t * cos(t)), t=0..2pi/2
yayyy involute curve yayy
