A four-bar linkage or simply a 4-bar or four-bar is the simplest movable linkage. It consists of four rigid bodies (called bars or links), each attached to two others by single joints or pivots to form closed loop.

**DYNAMIC
ANALYSIS OF FOUR BAR MECHANISM:**

A **four-bar linkage** or simply a **4-bar**
or **four-bar** is the simplest movable linkage. It consists of four rigid
bodies (called bars or links), each attached to two others by single joints or
pivots to form closed loop. Four-bars are simple mechanisms common in
mechanical engineering machine design and fall under the study of kinematics.

Dynamic
Analysis of Reciprocating engines.

Inertia
force and torque analysis by neglecting weight of connecting rod.

Velocity
and acceleration of piston.

Angular
velocity and Angular acceleration of
connecting rod.

Force
and Torque Analysis in reciprocating engine neglecting the weight of connecting
rod.

Equivalent
Dynamical System

Determination
of two masses of equivalent dynamical system

The inertia force is an imaginary force,
which when acts upon a rigid body, brings it in an equilibrium position. It is
numerically equal to the accelerating force in magnitude, but ** opposite**
in direction. Mathematically,

Inertia force = –
Accelerating force = – *m.a*

where *m *= Mass of the body, and

*a *=
Linear acceleration of the centre of gravity of the body.

Similarly, the inertia
torque is an imaginary torque, which when applied

upon
the rigid body, brings it in equilibrium position. It is equal to the
accelerating couple in magnitude but ** opposite** in direction.

**1
D-Alembert’s Principle**

Consider a rigid body
acted upon by a system of forces. The system may be reduced to a single
resultant force acting on the body whose magnitude is given

by the product of the
mass of the body and the linear acceleration of the centre of mass of the body.
According to Newton’s second law of motion,

*F *=*
m.a*

*F *= Resultant
force acting on the body,* *

*m *= Mass of the
body, and

= Linear acceleration of the centre of mass of the *a
*body.

The equation **( i)**
may also be written as:

*F *–*
m.a *= 0

A little consideration
will show, that if the quantity – *m.a* be treated as a force, equal,
opposite and with the same line of action as the resultant force *F*, and
include this force with the system of forces of which *F* is the
resultant, then the complete system of forces will be in equilibrium. This
principle is known as ** D-Alembert’s principle. **The equal
and opposite force

*F *+*
F*_{I}* *= 0...**( iii)**

Thus, D-Alembert’s
principle states that *the resultant force acting on a**body
together with the reversed effective force **( or inertia force),
are in equilibrium.*

This
principle is used to reduce a dynamic problem into an equivalent static
problem.

**2
Velocity and Acceleration of the Reciprocating Parts in Engines**

The velocity and
acceleration of the reciprocating parts of the steam engine or internal
combustion engine (briefly called as I.C. engine) may be determined by
graphical method or analytical method. The velocity and acceleration, by
graphical method, may be determined by one of the following constructions:

**1.
**Klien’s
construction,** 2. **Ritterhaus’s construction, and** 3. **Bennett’s** **construction.

We shall now discuss
these constructions, in detail, in the following pages.

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