Leonardo da Vinci (1938, 628) was no mathematician but he recognised its utility in understanding mechanics when he wrote: “Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruit of mathematics.” Mechanics, in fact, has always appealed both to the mathematician and to the practical man and so it is appropriate that both aspects should be considered, and that we should begin with the mechanics of simple machine elements.
In the beginning men and women relied on the strength of their own muscles to exert a force, but it is characteristic that they used tools to enhance this force to make it more effective. Prehistoric man prepared flints so that meat might be more easily cut, animals might be more readily killed, and trees felled without too much effort. Very soon muscles of animals were used for the more onerous tasks of dragging or carrying loads. In the first millennium B.C. the ballista, and the bow before that, used stored energy to throw projectiles over comparatively large distances. Boats were usually rowed but from the fourth millennium B.C. they could also be powered by the wind. It was not until the first century B.C. that an alternative prime mover, the water wheel, was invented. It was almost another millennium before the use of windmills became common, and another half millennium before steam power was developed. By any standard, this was slow progress. Of course prime movers could not evolve until the essential elements used in their construction were sufficiently developed and understood. It is the purpose of this and the subsequent chapter to give some account of the history and characteristics of these essential mechanical elements. They include levers, balances, inclined planes, wedges, screw threads, and pulleys, which are described in this chapter, and belt or rope drives, brakes, gears, cams, and bearings, which are the topic of the next chapter.
Power is the scalar product of force and velocity. A common feature of all machine elements, if friction losses are ignored, is that