## Introduction:

First of all, you should know what is dynamics of machines or machinery. The subject Dynamics of Machines (DOM) are derived from the "Theory of Machines". Let me explain it. Theory of Machines is the science which deals all related to machines. That is, displacement, velocity, acceleration, various forces acting on the machine parts and their effects are studies. From which some of the specific studies have been made and those are termed into different subcategories. DOM is such one. So the classification of Theory of Machines can be understood from the following diagram.

Dynamics deals with the study of forces and their motions of parts of machines, wheres as Kinematics deals with only the study of the motions (displacement, velocity and acceleration analysis only). So you may think what is kinetics. Kinetics is the science which deals with only the study of inertia forces and their effects. Now what should be the statics? It is simply defined as the study of body or machine parts under the rest (No external forces are acting)

## Some basic terminologies involved in the study of Static force analysis of mechanisms

Before going into analysis section, you must know,

- What is static force?
- What is dynamic force?
- What is inertia force?

*Static Force:*It is nothing but a force which is experienced due to the self weight or load of a body or parts of machine. Example: Hanging weights

*Dynamic Force:*It is a force that are found in the moving parts of a machine. Moving can be linear, rotation or some other means. Example: Forces in the rotating fan, prime movers, lathe in operation, drilling machines in operations and so on.

*Inertia Force:*It is an imaginary internal force of body which is created due to the rotating or reciprocating parts of a body. It resists any change in the status of motion of body. It has the tentency to keep the moving objects in a straight line. Ex: Moving cricket ball

*Equilibrium:*A body is to be in equilibrium when all the forces are in balance and no resulting acceleration presents in it.

Static Equilibrium: When a body is at rest, it tends to remain at rest. So there is no velocities. This status is called as static equilibrium. That is the body is statically balanced.

*Dynamic Equilibrium*: When a body is in motion, it tends to keep the motion. So the velocities exist but remains constant. This status is know to be dynamic equilibrium

*Newton's first law of forces*: Static and dynamic equilibrium are defined based on the newton's first law of motion. The law states that every body continues its state of rest or motion unless it is compelled to change its state by externally applied force.

*Conditions for equilibrium:*There are two conditions defined for equilibrium whether static or dynamics equilibrium.

- Vector or algebraic sum of all forces acting on a body must be zero
- The Vector or algebraic sum of all the moments of all forces about any point must be zero.

Mathematically, ΣF = 0, ΣM = 0, where F is resultant force, M is resultant moment

In case of planer mechanisms, the forces are being solved along two mutually perpendicular axes. So the equation are, ΣFx = 0, ΣFy = 0, ΣFM= 0

## Example for equilibrium - Equilibrium of two and three forces systems

Let us consider a body with two force system as shown in the Figure 1 and 2.

Here, consider two forces of different magnitude and action at different directions as shown in the figure. Since two forces are not equal and in different directions, the vector of sum of these forces will not be zero and hence they will be not in equilibrium. So a body under the action of forces will be in equilibrium when

- Two forces must be equal in magnitude
- They should act along the same line and in opposite direction to each other

These conditions are satisfied in the Figure 2 shown below and hence the forces in it are said to be in equilibrium.

Similarly, for a body under the action of three forces, the equilibrium status will be governed by the following rules,

- The resultant force of three forces must be zero
- The line of action of all the three forces must be meeting at a common point called as the "point of concurrency"

The respective figures are shown below.

Note: Moment about a point can be defined as the turning effect of a force about that point. It is measured using magnitude of force x the perpendicular distance between the force and the point.

## Free Body Diagrams

It can defined as the diagram which describes various parts of machines or mechanisms that are physically disconnected.. Each part or link will be in equilibrium when the whole system in equilibrium. F.B.D is an important toll in analyzing the forces in mechanisms. See the following example in which the all links are freely drawn by disconnecting from each other in a four bar mechanism.

## Methods of Static Force Analysis of Simple Mechanisms

There are generally three methods of the static force analysis. There are:

- Principle of Super position
- Method of normal and radial components
- Principal of virtual work

Let's see each method one by one.