Dynamic Analysis of Four Bar Mechanism

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 – m.a is known as reversed effective force or the inertia force (briefly written as F_I). The equation (ii) may be written as

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.