Curvature and torsion of a helix

Question

I would like to calculate the curvature and torsion for a helix knowing the radius $r$, pitch $2pπ$, center $s$, and direction axis $d$. Can anyone help? I know how to compute curvature and torsion for $H = r\cos(t),\space r\sin(t),\space z$.

Thank you

And what have you tried...? This should be in any textbook. – IAmNoOne Dec 21 '14 at 08:59 — IAmNoOne, Dec 21 '14 at 08:59

score 1 · Accepted Answer · answered Jan 14 '15 at 02:28

Curvature and torsion are independent of the location of the curve so we can ignore those factors. For a circular helix of radius $r$ and pitch $2\pi p$, we can parameterize it as follows:

$x(t) = r\cos(t),\, y(t) = r\sin(t),\, z(t) = pt.\,$

The curvature for a helix as defined above is $\frac{|r|}{r^2+p^2}$ and its torsion is $\frac{p}{r^2+p^2}.$

Curvature and torsion of a helix

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