ee ee Pee 
FRICTION AND LUBRICATION 271 
when P overcomes Q, and the lower sign when Q overcomes P, In this 
case R= P+Q. 
When @= 180°, OA and OB are in the same straight line, and P and 
Q are on the same side of O, then P= Q° a the upper sign to be taken 
when P overcomes Q, and the lower sla aa Q overcomes P. “In this 
case R= P-Q. 
237. Friction Axis of a Link.—The friction of a pin joint, such as 
is common in links or rods in mechanisms, is of the same character as the 
friction of an axle discussed in the preceding Article. It has been seen that 
in the case of an axle when the axle rotates in its bearing, or when the 
piece carried by the axle rotates on it, the resultant force on the axle 
does not intersect the axis, but is a tangent to its friction circle. So in a 
link, like the connecting-rod of a steam-engine, with pin joints at its ends, 
the line of thrust or pull on the rod will not coincide with the axis of the 
rod,* but will be tangential to the friction circles of the pins of its joints. 
This actual line of thrust or pull on the rod is called the friction axis of 
the rod or link, the change of the line of action of the thrust or pull from 
the geometrical axis of the rod to the friction axis being due to the 
friction of its pin joints. 
Since four tangents may in general be drawn to two circles, it follows 
that a rod with pin joints has four different possible friction axes, and the 
one which is to be taken in any particular case will depend on the diree- 
tions of the external forces on the link, ard on the directions of its 
motions relative to the pins of the joints or to the bearings of the pins. 
This point is made clear by Fig. 414, which shows the connecting-rod 
AB and the crank BC of a steam-engine in four different positions (a), 
(4), (c), and (d) during a revolution of the crank. 
The friction circles of the pins at A and B are shown greatly enlarged 
for the sake of clearness. In each position A’B’ is the friction axis of 
the connecting-rod. There is rotary motion of the pins in their bearings 
at A and B, and the point to be remembered is, that since friction always 
opposes motion, the force acting along the friction axis at a joint must 
have a moment about the axis of the pin to overcome the friction which 
tends to prevent the rotation at that joint. 
In the position (a), Fig. 414, where the connecting-rod is exerting a 
thrust on the pins at A and B, the angle BAC is increasing, and will go 
Saal Te ar a 
ae) OS 
Fra. 414. 
on increasing until the crank has turned through 90° from its inner 
* The axis of the rod is here the line joining the centres of the pin joints at 
its ends. 
