Hence, whatever the ratio ξ : η, the axis of the resultant screw lies on the conoidal surface
z (x2 + y2) = cxy,
(13)
where c = 1⁄2(k − h). The co-ordinates of any point on (13) may be written
x = r cos θ, y = r sin θ, z = c sin 2θ;
(14)
hence if we imagine a curve of sines to be traced on a circular cylinder so that the circumference just includes two complete undulations, a straight line cutting the axis of the cylinder at right angles and meeting this curve will generate the surface. This is called a cylindroid. Again, the pitch of the resultant screw is
p = (λξ + μη) / (ξ2 + η2) = h cos2 θ + k sin2 θ.
(15)
| From Sir Robert S. Ball’s Theory of Screws. |
| Fig. 41. |