A Screw-jack is a device used for lifting heavy weights or loads with the help of a small effort applied at its handle. The followings are two types of screw-jack:

(a) Simple screw-jack, and

(b) Differential screw-jack.

**3.9.1 Simple Screw-Jack. **Fig. 3.48 shows the simple screw jack, which consist of a nut, a screw the square threads and a handle fitted to the head of the screw. The nut also forms the body of the jack.

Fig. 3.48. Simple screw-jack

The load to be lifted is placed on the head of the screw. At the end of the handle, fitted to the screw head, an effort P is applied in the horizontal direction to lift the load W. The screw-jack works on the same principle on which an inclined plane works.

Let W = Weight placed on screw head,

P = Effort applied at the end of the handle,

L = Length of handle,

p = Pitch of the screw,

d = Mean diameter of the screw,

α = Angle of the screw or helix angle,

Φ = Angle of friction,

µ = Co-efficient of friction between screw and nut = tan Φ

When the handle is rotated through one complete turn, the screw is also rotated through one turn. Then the load is lifted by a height p (pitch of screw).

The development of one complete turn of a screw thread is shown in Fig. 3.49 (a). This is similar to the inclined plane. The distance AB will be equal to the circumference (πd) and distance BC will be equal to the pitch (p) of the screw. From the Fig. 3.49 (a), we have

Let R = Normal reaction

F = Force of friction = µR

As the load W is lifted upwards, the force of friction will be acting downwards. All the forces acting on the body are shown in Fig. 3.49 (b).

**Problem 3.40. ***(a) Find the effort required to apply at the end of a handle, fitted to the screw head of a screw-jack to lift a load of 1500 N. The length of the handle is 70 cm. The mean diameter and the pitch of the screw-jack are 6 cm and 0.9 cm respectively. The co-efficient of friction is given as 0.095.*

*(b) If instead of raising the load of 1500 N, the same load is lowered, determine the effort required to apply at the end of the handle.*

**Problem 3.44.*** A screw-jack has a square thread, 7.5 cm mean diameter and 1.5 cm pitch. The load on the jack revolves with the screw. The co-efficient of friction at the screw threads is 0.05.*

*(i) **Find the tangential force to be applied to the jack at 36 cm radius so as to lift a load of 600 N.*

*(ii) **State whether the jack is self-lacking. If it is, find the torque necessary to lower the load. If not, find the torque, which must be applied to keep the load from descending.*

(AMIE Winter, 1981 ; U.P.Tech. University, 2002-2003)

**Problem 3.45.*** A screw-jack has a square thread of mean diameter 6 cm and pitch 0.8 cm. The coefficient of friction at the screw thread is 0.09. A load of 4 kN is to be lifted through 12 cm. Determine the torque required and the work done is lifting the load through 12 cm. Find the efficiency of the jack also.*

**Sol. **Given:

**3.9.2. Differential Screw-Jack.** Fig. 3.52 shows a differential screw-jack. The principle, on which this machine works, is the same as that of any other differential machine, i.e., action of one part of the machine is subtracted from the action of another part.

The differential screw is in two parts, A and B. Part A is threaded both on inside and outside ; whereas the part B is threaded on the outside only. The external threads of A gear with the threads of the nut C, which form the body of the differential screw-jack. The internal threads of A gear with the threads of the nut C, which form the body of the differential screw-jack. The internal threads of A gear with the external threads of the screw B. Thus the part A behaves as a screw for the nut C and as a nut for the screw B.

The screw B does not rotate, but moves in vertical direction only, and carries the load. When the effort is applied at the lever, the screw A rises up and simultaneously the screw B goes down. Thus the net life of the load is algebraic sum of the motions of the screw A and screw B.

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