A Treatise on the Theory of Screws

132 THE THEORY OF SCREWS. [144, By similar triangles, Q AO rrr\ 2 -‘I rrrt . aß OH ’ ' ~ W HH'**"’ Fig. 24. _ OA . O'H O'H2 whence or - aß QH oc 2 , OH or, as before (§141), co x Qjj • It will be noticed that, for this investigation, H may have been chosen arbitrarily on the circle. We thus see that, besides the two points 0 and 0, there will be a system of pairs of points of which any one may be employed for finding the instantaneous screw, and for determining the instantaneous twist velocity. If we choose any two points (Fig. 25), Il and fl', so that (Zfin'F) = (XOO'F); then A being given, determines H, and H£l' determines A', while the twist velocity is proportional to O' H -rWe can suppose fl at infinity,