A Treatise on the Theory of Screws

___________ ______ ____________ __________ _______ _______ _________ 65] THE REPRESENTATION OF THE CYL1NDRO1D BY A CIRCLE. 50 but we know (§ 59) n, =---:__” • 5 ’ 11 2S0 ’ whence the virtual coefficient is A 0 . BX _ 2m sin A . A 0 OG 2S0~ 2SO ~m OS ’ as already determined. This is an instructive proof, besides being much shorter than the other methods. 64. Properties of the Virtual Coefficient. If the virtual coefficient be given then the chord envelopes a circle with its centre at the pole of the axis of pitch. Two screws can generally be found which have a given virtual coefficient with a given screw. Let A (Fig. 15) be a given screw, and X a variable screw ; then their virtual coefficient is proportional to OG, and therefore to the sine of A, that is, to the length BX. Thus, as X varies, its virtual coefficient with A varies proportionally to the distance of Å from the fixed point B. 65. Another Construction for the Pitch. As the virtual coefficient of two coincident screws is equal to their pitch, we shall obtain another geometrical construction for the pitch by supposing two screws to coalesce. For (in tig- 16), let A G bo the chord joining the two coincident screws, that is the tangent, then, from § 61, we have for the pitch, OG m 0^, whence the following theorem :— The pitch of tiny screw is proportional to the perpendicular on the tangent at the point let fall from the pole oj the axis oj pitch. __________________________ ___________________________________________________________________________________