Force Analysis

Unit: IV

Force Analysis

Chapter 10: Static Force Analysis

Chapter 11: Dynamic Force Analysis

Chapter: 10

Static Force Analysis

Learning Objectives

While reading and after studying this chapter, you will be able to:

• Differentiate between static force analysis and dynamic force analysis. 

• Understand the conditions for static equilibrium.

• Describe the equilibrium of two-force, three-force and four-force members. 

• Determine the various forces on the links and the torque applied, when a four-bar mechanism is subjected to an external force on any of its links.

• Perform the static force analysis in slider-crank mechanism with two known forces.

SYLLABUS

Static force analysis - Static equilibrium of two-force, three-force members - Applied and constraint forces - Free body diagram - Static force analysis of simple planar mechanisms

INTRODUCTION

In all the previous chapters, we limited ourselves to consideration of the geometry of the motions and of the relationships between displacement and time. But the force required to produce those motions were not considered.

In the design of machine mechanisms, it is very essential to know the magnitudes and the directions of forces transmitted from the input to the output. We know that all machine members are subjected to different types of forces such as forces due to external loads, forces due to combustion of fuels, forces due to friction forces, forces due to change of temperatures, spring forces, impact forces, inertia forces, etc. Thus force analysis helps the designer in selecting proper sizes of the machine components to withstand the stresses developed in them.

In this chapter, we shall discuss the static force analysis of planar mechanisms in detail. 

1. Static Force Analysis

• When the inertia effect due to the mass of the machine components are neglected, then the analysis of mechanism is called as static force analysis.

• We know that inertia forces are produced due to the masses of the rotating/reciprocating components of a machine. However, if the magnitudes of these forces are small compared to the externally applied loads, they can be neglected while analyzing the mechanism. This type of analysis is known as static force analysis.

• Example: In hydraulic lifting cranes, the magnitude of inertia force due to weight of the hoisting hook is small compared to the externally applied loads. Thus the analysis of forces, neglecting the inertia force due to weight of the hook, is an example for static force analysis.

2. Dynamic Force Analysis

• When the inertia effect due to the mass of the components is also considered in addition to the externally applied loads, it is called dynamic force analysis.

• Example: In high speed IC engines, it is necessary to consider the effect of inertia forces (arising due to the mass of piston and connecting rod). Because the mass of the accelerating mass and thereby the inertia force is more, which should not ignored.

• The fundamental units in kinematic analysis are length and time. In dynamic analysis they are length, time and force.

Now let us discuss the static force analysis first.