194 THE INERTIA OF THE CONNECTING ROD — MACGREGOR. 



inertia be not sufficiently great for this purpose, fluctuations of 

 speed will occur, which, apart from the solution of the present 

 problem, may be determined approximately. We may therefore 

 regard the velocity of the crank -pin A as known for all positions 

 of the crank. 



The motion of the connecting- rod is thus one of the data of 

 the problem. As is well known, it may be regarded as rotating 

 instantaneously about a fixed axis whose position is the inter- 

 section 0, of the line CA produced, with a line through B per- 

 pendicular to BC. The distances of from A and B for any 

 position of the crank may be found by drawing to scale a dia- 

 gram similar to Fig. 1 and measuring the lengths of the lines A 

 and BO. We shall use the symbols s and jj to indicate these 

 distances respectively. 



The forces acting on the connecting rod are (its weight being- 

 neglected) the force exerted on the end B by the crosshead of the 

 piston rod, and the resistance of the crank-pin acting on the end 



A, which is of course equal and opposite to the force exerted by 

 the rod on the crank-pin. As we are neglecting friction, these 

 forces may be considered as acting through the points B an<l A, 

 the centres of the pins. They may be resolved into components 

 in and perpendicular to the lines of motion of B and A respect- 

 ively. Let P and (S be the components in the lines of motion. 

 The indicator diagram, the area of the piston, and the mass of 

 the reciprocating parts, being given, P may readily be deter- 

 mined for all positions of the crank. S is the force which it is 

 desired to determine. 



The simplest relation between these forces and the kinetic 

 changes which the connecting rod is given as undergoing, is that 

 expressed in the ecjuation of energy. Let dc be the length of 

 arc described by the crank-pin A, during any small displacement 

 of the rod. Then, as the rod is instantaneously rotating about 

 0, (p/s)dc will be the distance traversed in the same time by 



B. Hence the work done by the forces acting on the rod is 



P('PIs)cIc — Sdc ; 

 for the component forces perpendicular to the lines of motion of 

 A and B do no work. The work done must be equal to the in- 



