Farm Machinery and Equipment. Harris Pearson Smith
When one or more fixed pulleys and one or more movable pulleys (Fig. 3–4) are used in combination, they form the block and tackle. The mechanical advantage varies directly as the number of ropes that support the movable pulley and the weight,
w × h = F × 3h
or
where w = weight
h = distance weight moves
F = force applied
3 = number of ropes supporting w
The differential pulley (Fig. 3–5) is a modification of a block and tackle but differs in that the two pulleys D and C are of different radii and rotate as one piece about a fixed axis B. The endless chain passes under and supports the movable pulley G and any weight attached to it. To raise a load, force is applied downward to chain F, which will rotate pulleys C, D, and G, causing the chain to wind up on the larger fixed pulley D and unwind on the smaller fixed pulley C, thus raising movable pulley G. In operation consider that point D of the section of chain DH moves up through an arc whose length is equal to BD. At the same time the point C of the section of chain CA will move downward an arc, a distance equal to BC. The length of the chain loop DHAC will be shortened to BD — BC, which will cause pulley G to be raised half this amount. P, the pulley force, is then applied to the section of chain EF, and the weight W is lifted at G. The mechanical advantage will be
FIG. 3–4. Block and tackle.
FIG. 3–5. Differential hoist.
FIG. 3–6. Geared differential hoists: A, worm-geared hoist; B, planetary-geared hoist.
P × BD = W × 1/2((BD — BC)
Figure 3–6 shows a geared differential hoist.
Inclined Plane. The inclined plane, shown in Fig. 3–7, is an even surface sloping at any angle between the horizontal and the vertical. The law or principle which governs the inclined plane in mechanics is that the force applied is increased as many times as the length of the inclined plane is greater than the elevation H. Briefly, it is equal to the length over the height, varying with the direction in which the force is applied. Instead of lifting the entire weight of the object vertically, part is supported on the plane and part by the force. Referring to Fig. 3–7, if the force F causes the weight W to move from A to C and parallel to the plane, the work done is F times AC, while the work done against gravity is the weight W times CE, if friction is disregarded, or briefly,
FIG. 3–7. The inclined plane.
FIG. 3–8. Screw.
F × AC = W × CE
If the force is parallel to the base AE, the advantage would be
F × AE = W × CE
Screw. The screw (Fig. 3–8) is the application or modification of the inclined plane combined with the lever. The threads winding around a cylinder bear the same relation to the inclined plane that a winding staircase bears to a straight one. When the screw is turned on its axis with the aid of a lever or gear, its sloping thread causes the load to move slowly in the direction of its vertical axis. The vertical distance between threads is called the pitch of the screw. The mechanical advantage is figured upon the condition that the applied force moves through a distance equal to the circumference of a circle whose radius is the length of the jackscrew bar or the radius of the driving gear, while the weight is being moved through a distance equal to the pitch of the screw.
Wedge. The wedge is a modification of the inclined plane. Actually it consists of two inclined planes placed base to base (Fig. 3–9). The force pushing on the wedge into any material, such as a log, will cause forces to act perpendicular to each of the two faces of the wedge.
FIG. 3–9. Wedge.
REFERENCES
Clyde, A. W.: Mechanics of Farm Machinery, Farm Impl. News, January to March, 1944.
QUESTIONS AND PROBLEMS
1. In Fig. 3–2A, a force of 80 pounds is exerted at W; l = 12 inches and L = 32 inches. Find the value of force F required to balance the lever.
2. In Fig. 3–2B, a weight of 90 pounds is supported at W; l is 10 inches. The total length of L of the lever is 25 inches. Find the value of F.
3. In Fig. 3–2C, F = 28 pounds; L = 10 inches, A = 24 inches. What is the weight supported at W?
4. The radius of a roller on which is wound the lifting rope of a windlass is 4 inches. What force must be exerted at the end of a crank arm 24 inches in length attached to the shaft to lift one ton (2,000 pounds)? W = 2,000; R — 24; r = 4 (Fig. 3–3).
5. In Fig. 3–4 is shown a block and tackle. The pulleys turn freely on a pin. There are three parts of rope. If 90 pounds is to be lifted, what force is required at the end of the rope F?
CHAPTER 4
TRANSMISSION OF POWER AND COMPONENT PARTS OF MACHINES
The method of transmitting power from its source to the point of use is one of the greatest problems of the farm-equipment designer. The problem is relatively simple when a tractor is used to operate a threshing machine. The size and speed of the pulleys on the two units are approximately the same. The tractor pulley is lined up with the thresher pulley, and a flat belt is fitted over them and tightened by backing the tractor. The power is ready to be transmitted from the tractor to the thresher.