Fig. 3308.
An eccentric is the exact equivalent of a crank having the same amount of throw, as may be seen from [Fig. 3308], in which the outer dotted circle represents the path of the crank and the inner one the path of the centre of the eccentric. A small crank is marked in, having the same throw as the eccentric has, and the motion given by this small crank is precisely the same as that given by the eccentric whose outer circumference is denoted by the full circle.
Considering the motion of both the crank and the eccentric, therefore, we may treat them precisely the same as two levers, placed a certain distance apart, revolving upon the same centre (the centre of the crank shaft), and represented by their throw-lines.
Fig. 3309.
In [Fig. 3309], let the full circle e e represent an eccentric upon a shaft whose centre is at c, and let the centre of the eccentric be at e. The path of revolution of the eccentric centre will be that of the dotted circle whose diameter is b, d. As the eccentric is in mid-position (e being equidistant from b and d), the valve will be in mid-position as denoted by the full lines at the bottom of the figure. Now suppose the eccentric to be revolved on the centre c, until its centre moves from e to v, its circumference being denoted by the dotted circle a a, and if we draw from v a vertical line cutting the line b, d at f, then from c to f will be the distance the eccentric would move the valve, which would then be in the position denoted by the dotted lines at the bottom of the figure. It becomes clear then that if we suppose the eccentric to have moved from mid-position to any other position, we may find how much it will have moved the valve by first drawing a circle representing the path of the centre of the eccentric, next drawing a line (as b d) through its centre, and then drawing a vertical line as (c e) through its mid-position and also a vertical line from the eccentric centre in its new position, the distance between these two vertical lines (as distance c f in the figure) being the amount the eccentric will have moved the valve.
It may have been noticed that the diameter of the eccentric does not affect the case, the distance b d, or the diameter of the circle described by the centre of the eccentric, being that which determines the amount of valve motion in all cases. This being the case, we may use the circle representing the path of the eccentric centre for tracing out the valve movement without drawing the full eccentric, and the diameter of that circle will of course equal the full travel of the valve.
The position of an eccentric upon a shaft is often given in degrees of angle, which is very convenient in some cases. If a valve has no lap or lead, the eccentric will stand at a right angle or angle of 90 degrees when the crank is on the dead centre.