The Theory of Machines (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1917 Excerpt: ...being in the same direction. Should AB exceed F = fN there would be acceleration, and should it be less than/iV there would be no motion. Now from Fig. 109, AB = R sin f, and also AB = BC tan f, = N tan 4, . Hence, since AB = fN, there results the relation fN = N tan or / = tan; this is to say, in order that two bodies may have relative motion at uniform velocity, the resultant force must act at an angle f, to the normal to the rubbing surfaces, and on such a side of the normal as to have a resolved part in the direction of motion. The angle cj is fixed by the fact that its tangent is the friction factor /. 168. Angle of Friction.--The angle c may be conveniently called the angle of friction and wherever the symbol c occurs in the rest of this chapter it stands for the angle of friction and is such that its tangent is the friction factor /. The angle 4 is, of course, the limiting inclination of the resultant to the normal and if the resultant act at any other angle less than cf, to the normal, motion will not occur; whereas if it should act at an angle greater than 4 there will be accelerated motion, for the simple reason that in the latter case, the resolved part of the resultant parallel to the surfaces would exceed the frictional resistance, and there would then be an unbalanced force to cause acceleration. 169. Examples.--A few examples should make the principles clear, and in those first given all friction is neglected except that Fig. 110.--Crosshead. in the sliding pair. The friction in other parts will be considered later. 1. As an illustration, take an engine crosshead moving to the right under the steam pressure P acting on the piston, Fig. 110. The forces acting on the crosshead are the steam pressure P, the thrust Q due ...