PULLEY (OF., Fr. poulie, probably from LGer. paten, AS. pullian, Eng. pull). A circu lar wheel turning on a smooth axle through its centre, and with a grooved cut in its rim so that a cord can run around it. A 'fixed' pulley is one whose axle is fixed to some support; while a free pulley is not stationary, but is carried in the bight of the cord passing over it. A fixed pulley simply changes the direction of the force which the cord exerts. if in Fig. I F, and are two forces acting on a cord passing over a pulley, they will be equal if the system is in equilibrium.
If a free pulley carrying a weight is supported by a cord, as shown in Fig. 2. there are three forces acting on the pulley. a force F, vertically down equal to the weight of the pulley and the weight it carries, and two forces obliquely up ward each equal to F, due to the two branches of the cord which passes over the pulley. If the branches of the cord make an angle 0 with the vertical, 2F,cos8 is the total force acting verti eally upward; therefore if there is equilibrium 2F,cos8 = and the mechanical advantage, – is 2cos8. In particular, if, as is usually
the case, the two branches of the cord are parallel and vertical, 8 = 0, and 2E, = This same formula may be deduced by consider ing the system displaced slightly from equilib rium, using the principle of the conservation of energy.
Fixed and free pulleys may be combined in many ways, but the principle is evident. If a continuous cord passes over a free compound pulley—made up of several independent wheels— in such a manner that there are a supporting brandies of the cord, the mechanical advantage is a.
Pulleys are also made in which two toothed wheels of different radii are clamped together, so that as one turns the other must also; and the cord is replaced by a chain whose links fit into the teeth. Such a pulley is called a 'differ ential' one If one wheel has in its rim N teeth. and the other N-1, the mechanical ad ntage is 2N.
The principle of the action of pulleys was first given by Stevinus. See BLOCK; TACKLE.