Introduction to Dynamics of Machinery , Static force analysis, dynamic force analysis

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: