This document provides an overview of static force analysis in machinery dynamics. It introduces key concepts like inertia force, inertia torque, and static versus dynamic force analysis. Static force analysis neglects inertia forces, while dynamic analysis considers them. Free body diagrams are used to determine the nature and direction of forces acting on machine components in static equilibrium. Mass moment of inertia is a measure of an object's resistance to changes in rotation. The document provides examples of force equilibrium conditions for members under various force configurations.

1. Dynamics of
Machinery
Static Force Analysis
Mr.P.D.Devan
Assistant Professor
Kumaraguru College of Technology
Coimbatore

2. Overview of
this Lecture
• Introduction
• Inertia Force
• Inertia Torque
• Static Force Analysis
• Dynamic Force Analysis
• Problem-1

3. Introduction

4. Cont…
• All the mechanisms / machines has moving parts / links to
transmit force.
• It is must to know the force direction and magnitude to
design the elements.
• Selection of proper size of element is very important to
withstand stresses.
• If not ----→ machine / elements will fail.
• If has more strength-----→ cannot meet other requirements.

5. Inertia Force
• If machine components accelerates,
inertia forces are produced due to
masses.
• A force opposite in direction to an
accelerating force acting on a body
and equal to the product of the
accelerating force and the mass of the
body.
• −F = ma

6. Static Force Analysis
• Magnitude of the inertia force is
less than the applied force
• Inertia forces are neglected

7. Dynamic Force
Analysis
• When the inertia forces are considered
in the analysis of the mechanism, the
analysis is known as dynamic force
analysis.
• Magnitude of inertia forces are large
compared with applied forces.
• Applying D’Alembert principle.

8. Inertia Torque
(Inertia Couple)
• It is an imaginary torque,
which when applied on a
rigid body, brings it in to
equilibrium.
• Equal to the accelerating
couple but in opposite sense.

9. Mass Moment of Inertia
• Measure of distribution of mass of a rigid body w.r.t. the
axis.
• It is a measure of an object’s resistance to changes to its
rotation.
• Capacity of a cross-section to resist bending
• It must be specified with respect to a chosen axis of rotation

11. Equilibrium of Two Force
Members
• A member under the action of two forces will be in
• equilibrium if
–the forces are of the same magnitude
– the forces act along the same line
– the forces are in opposite directions.

12. Equilibrium of Three
Force Members
• A member under the action of
three forces will be in equilibrium
if
– the resultant of the forces is zero
– the lines of action of the forces
intersect at a point (point of
concurrency).

13. Member with Two
Forces and Torque
• A member under the action of two forces and an
applied torque will be in equilibrium if
– the forces are equal in magnitude, parallel in
direction and opposite in sense
– the forces form a couple which is equal and
opposite to the applied torque.

14. Member
with Four
Forces

15. Member with Three or More Parallel Forces

16. Force
convention

17. Free body diagrams
• A free body diagram is a sketch or diagram of a part isolated from the mechanism in order to
determine the nature of forces acting on it.
• As the mechanism is in static equilibrium, each of its members must be in equilibrium
individually.
• Member 4 is acted upon by three forces F, F34 and F14.
• Member 3 is acted upon by two forces F23 and F43.
• Member 2 is acted upon by two forces F32 and F12 and a torque T.
• Link 3 is a two-force member and for its equilibrium F23 and F43 must act along BC.
• F34 being equal and opposite to F43 also acts along BC.

18. Cont…
• Initially, the direction and sense of some forces are unknown.
Link 4:
• Assume that the force F is known.
• To know other two forces the direction of one or more force must be known.
• F14 passes through the intersection of F and F34 .
Link 3:
• It is a two force member (F23,F43) acts along BC.
• F43 and F34 are equal and opposite.
Force Triangle:
• F43 = F34 = F23 = F32
• Link 2 in equilibrium if F12 = F32
• T = F12 x h = F32 x h

19. Problem 1: