Theory of Machines-I

Theory of Machine is that branch of science which deals with the study of relative motion between the various parts of a machine, and forces which act on them. Theory of machine may be divided into kinematics and dynamics. Kinematics is that branch of theory of machine which deals with the study of relative motion between the various parts of the machines. Here the various forces involved in the motion, are not considered. Thus kinematics is the study to know the displacement, velocity and acceleration of a part of the machine.

The velocity of various points in a mechanism, is determined by (i) relative velocity method and (ii) the instantaneous centre method, provided we know the velocity at one point. The velocity analysis is necessary for determining the acceleration of the points in the mechanism. The choice of the method depends upon the nature of the mechanism and accuracy required. In this chapter both the above methods are discussed.

If the velocities of various points in a mechanism are known, then the acceleration of these points can be easily determined. After knowing acceleration the force, which is the product of mass and acceleration, can be obtained. From the forces, the stresses (which are equal to force divided by area) at the various points of the mechanism will be known. These stresses are in addition to the stresses caused by the working loads. With increasing speeds, higher and higher accelerations are being called for. Hence the forces and stresses due to higher accelerations are sometimes more than the stresses caused by the working loads. As acceleration is proportional to the square of the speed, i.e., acceleration = ω2 × r, hence if the speed of the machines becomes two times, the centripetal force will become four times. Thus the acceleration diagrams are, therefore, fundamental to stress analysis of mechanism.

When the two elements of a pair have a surface contact and a relative motion takes place, the surface of one element slides over the surface of the other, the pair is known as lower pair. This chapter deals with such mechanism having lower pairs. Lower pairs generally comprise turning pairs and sliding pairs. The mechanism having lower pairs are pantographs, an exact straight-line mechanism, an approximate straight-line mechanism, steering gear mechanism and universal or Hooke’s joint.

When a solid body slides over a stationary solid body, a force is exerted at the surface of contact by the stationary body on the moving body. This force is called the force of friction and is always acting in the direction opposite to the direction of motion. The property of the bodies by virtue of which a force is exerted by a stationary body on the moving body to resist the motion of the moving body is called friction. Friction acts parallel to the surface of contact and depends upon the nature of surface of contact.

A brake is a device used either to bring to rest a body which is in motion or to hold a body in a state of rest or of uniform motion against the action of external forces or couples. Actually the brake offers the frictional resistance to the moving body and this frictional resistance retards the motion and the body comes to rest. In this process, the kinetic energy of the body is absorbed by brakes.

A rotating machine element, which gives reciprocating or oscillating motion to a second element is known as a cam. The second element is called a follower. Hence a cam is a mechanical member which is used to impart desired motion to a follower by direct contact. The cam rotates usually at constant speed and drives the follower whose motion depends upon the shape of the cam. Almost always the cam is the driver and the follower is the driven. The cams are commonly used in internal combustion engines (for operating the inlet and exhaust valves), in printing machinery, in machine tools, in automatic machines etc.

The motion from one shaft to another shaft may be transmitted with belts, ropes and chains. These method are mostly used when the two shafts are having long centre distance. But if the distance between the two shafts is very small, then gears are used to transmit motion from one shaft to another. In case of belts and ropes, the drive is not positive. There is slip and creep which reduces velocity ratio. But gear drive is a positive and smooth drive, which transmits exact velocity ratio. The gear is defined as a toothed element which is used for transmitting rotary motion from one shaft to another.

A combination of two or more gears, which are arranged in such a way that power is transmitted from a driving shaft to a driven shaft, is known a gear train. This term is generally applied to mean more than two gears in mesh between the driving shaft and the driven shaft. The gear train may consist of spur, bevel or spiral gears.