Introduction to Mechanics of MACHINES.

Theory of Machines may be defined as that branch of Engineering-science, which deals with the study of relative motion between the various parts of a machine, and forces which act on them.

The Theory of Machines may be sub-divided into the following four branches :

The study of machines or simple mechanisms , and the analysis of these parts connected together with links and pivots and levers is the theory of it.
We could say that the geometrical analysis which includes the locating of the centre of gravity of the whole mechanism is what it is.  It's is also the study of the effects of forces or loads or and torque on these objects through bending moment and force diagrams .

1. Kinematics. It is that branch of Theory of Machines which deals with the relative motion between the various parts of the machines.
2. Dynamics. It is that branch of Theory of Machines which deals with the forces and their effects, while acting upon the machine parts in motion.
3. Kinetics. It is that branch of Theory of Machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts.
4. Statics. It is that branch of Theory of Machines which deals with the forces and their effects while the ma- chine parts are at rest. The mass of the parts is assumed to be negligible.

Mechanics of Machines

The subject Mechanics of Machines may be defined as that branch of Engineering science which deals with the study of relative motion between the various parts of a machine and forces which act on these parts due to constrained motion. The study of relative motion alone is referred to as Kinematics while that of forces acting on these parts is called dynamics.

Kinematics

 Velocity: This is defined as the rate of change of displacement linear and angular of a body with respect to the time. Velocity is a vector quantity, to specify it completely the magnitude, direction and sense must be known. Acceleration: The acceleration of a body is the rate of change of its velocity linear or angular with respect to time. A body accelerates if there is a change in either the magnitude, direction or sense of its velocity and can thus accelerates without change in speed, as in the case of a body moving in a circular path with uniform speed.

Displacement: Displacement is defined as the distance moved by a body with respect to a certain fixed point. The displacement may be along a straight or a curved path. Equations of Uniformly accelerated Motion.

Let a body having linear motion accelerates uniformly from an initial velocity u to a final velocity v in time t; let the acceleration be a and the distance from the initial position be s. Then V= u + at

 S = ut + at2 ,

 V2 = u2 + 2as

The corresponding equations for angular motion are:

ὠ =ꭃ + at

ꝋ = ꭃ t + ½ a t 2 ,

 then its angular velocity, ὠ =  2πN/60 rad/ s.