Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
UNIT 4 FLYWHEEL
Flywheel
Structure
4.1
Introduction
Objectives
4.2
Dynamically Equivalent System
4.3
Turning Moment Diagram
4.3.1
Turning Moment Diagram of a Single Cylinder 4storke IC Engine
4.3.2
Turning Moment Diagram of a Multicylinder 4stroke IC En
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Kinematics and
Dynamics
BITS Pilani
Pilani Campus
Sachin U Belgamwar
Methods for velocity analysis
Kinematics: To deal with the relative motion of various element of
mechanism without taking into consideration the forces
producing the motion.
Graphical me
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Kinematics and
Dynamics
BITS Pilani
Pilani Campus
Radial CAM Nomenclature
BITS Pilani, Pilani Campus
Description of the follower
movement
1.
Rise movement of the follower away from the cam centre
2.
Dwell no movement of the follower
3.
Return movement
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Kinematics and
Dynamics
BITS Pilani
Pilani Campus
Sachin U Belgamwar
Velocity of the ram S
= 4.5 m/s
wrs =vrs /RS=4.67 rad/s
P
vpo
Figure shows the quick return mechanism of the
slotted lever. The various dimensions of the
mechanism are
OA=400mm,OP=200mm,
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
ME/MF F244
Kinematics and Dynamics of Machines
BITS Pilani
Pilani Campus
J S Rathore
Department of Mechanical Engineering
1
Kinematics and Dynamics of machines
Mechanics
Statics
Structure
No relative motion
F
2
Dynamics
Kinematics
Kinetics
Mechanism
M
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Dynamics of Reciprocating Engine
Lecture 3
J S Rathore
Dynamics of reciprocating engine:
( pgas A ma p )
A
Q
l
Revise
B
r
Qt
Q
M
O
xp N
Connecting rod is subjected to :
Continuous tensile and compressive stresses
Inertial torque
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Analytical solutions of velocity and acceleration
Lecture 1
Dr J S Rathore
Analysis of Kinematic quantities
1.
2.
3.
4.
Four bar mechanism
Slidercrank mechanism
Shaper (Quickreturn) mechanism
Cam mechanism
Displacement/Position
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Flywheel
Lecture 2
J S Rathore
Principle of Flywheel:
Mmean/demand/required
Flywheel is extra inertia, used
to reduce the fluctuation in
crankshaft speed
Max change in energy during
one cycle
Amount of energy stored in
flywheel
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Kinematics and
Dynamics
BITS Pilani
Pilani Campus
Radial CAM Nomenclature
BITS Pilani, Pilani Campus
Description of the follower
movement
1.
Rise movement of the follower away from the cam centre
2.
Dwell no movement of the follower
3.
Return movement
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
A shaft is supported in bearings 1.8 m apart and projects 0.45 m beyond bearings at each end.
The shaft carries three pulleys one at each end and one at middle of its length. The mass of
the end pulleys are 48 kg and 20 kg and their centers of mass are 15
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Dynamic Force Analysis
Lecture18 and 19
J S Rathore
Static Force analysis:
F ma cg
M J cg
F 0
M 0
Two or three force members
FBD of links
Pin reactions
Stress analysis and dimensions of links
Dynamic analysis has to be carrie
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI
FIRST SEMESTER 20102011
Comprehensive Examination
SOLUTION
(Closed Book)
KINEMATICS & DYNAMICS OF MACHINES
MF C313
Date: 1210
Max Marks: 40
Q1:
a) Governor acts as a mechanical control and feedback syst
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Gear Drives
Toothed wheels, which transmit power and motion
from one shaft to another by means of successive
engagement of teeth.
Most suitable drive, if the centre distance is small
It is a positive drive, velocity ratio remains
constant.
The efficie
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
DYNAMICS OF RECIPROCATING
ENGINES:
x AD AE ED
OA OE C1 D C1 E
r 1 Cos l l r Sin
r 1 Cos l r l r Sin
x r 1 Cos n n Sin
r rCos l C1C 2 CE 2
2
2
2
2
2
2
2
2
If n 1
x r 1 Cos
Piston Velocity
Sin 2
V p r Sin
2 n 2 Sin 2
Sin 2
r Sin
2n
If n 1
V p
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
Instruction Division
Date:08/01/2013
In addition to PartI (General Handout for all courses appended to the time table) this portion
gives further specific details regarding the course.
Course
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
> # Kinematics and Dynamics of Machines
Shantanab Dinda
2009B2AB764P
> start;
#Q1. Position Analysis of a Five Bar Mechanism
> N:=5;
> eq1:=sum(r[i]*cos(theta[i]),i=1.N); eq2:=sum(r[i]*sin(theta[i]),i=1.N);
> # The following are unknown: r[4] and theta[3]
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI
FIRST SEMESTER 20102011
Comprehensive Examination
(Closed Book)
KINEMATICS & DYNAMICS OF MACHINES
Date: 131210
MF C 313
Duration: 3 Hours
Max
Marks: 40
Be concise. Be legible. Answer all parts of a quest
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
KINEMATICS & DYNAMICS
OF MACHINES
STATIC FORCE ANALYSIS
When component of machine accelerates,
inertia forces and torques are produced due to
their masses.
In many situations, the magnitude of these
forces are small compared to externally
applied loads
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI
MF C313: KINEMATICS & DYNAMICS OF MACHINES
FIRST SEMESTER 20112012
Assignment  8
Dear Students,
Please note that there is some change in the problem(s) allotted to you. The assignment8 and
distribution
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Balancing
Lecture 1
J S Rathore
Objectives:
1. Rotating and Reciprocating unbalance
2. Importance of balancing in mechanical systems
3. Statically and Dynamically balanced system
4. Internal Balancing (Single plane balancing)
Ex
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Static Force analysis:
F ma cg
M J cg
F 0
M 0
Two or three force members
FBD of links
Pin reactions
Stress analysis and dimensions of links
Dynamic analysis has to be carried out
1) Situations, where inertial forces are comparable
with magnitudes of ex
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Introduction to Kinematics
Lecture 1 and 2
Terminology
Structure, mechanism and machine
Kinematic chain
Links
Kinematic pairs/joints
Four link planar mechanism/Slidercrank mechanism
Mobility and Degree of freedom : Kutzbac
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
GYROSCOPE ACTION IN MACHINES
Lecture by
Dr. Sharad Shrivastava
28.04.2015
Gyroscopic Couple
Consider a disc spinning with an angular velocity
rad/s about the axis of spin OX, in anticlockwise
direction when seen from the front;
Change in angular momentum
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Gyroscopic Couple
Consider a disc spinning with an angular velocity
rad/s about the axis of spin OX, in anticlockwise
direction when seen from the front;
Change in angular momentum;
and rate of change of angular momentum
In the limit when t 0,
Gyroscopic
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI
ME/MF F 244: Kinematics and Dynamics of Machines
SECOND SEMESTER 20142015
Tutorial  4 (Solution Key)
Duration: 50 mins
Date: 24th Feb15
Max Marks: 10
Q1. In the mechanism shown in Fig, the crank OA driv
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Static and Dynamic Force Analysis
Lecture1
J S Rathore
Force Analysis:
F ma cg
M J cg
Dynamic force analysis
1) Situations, where dynamic forces are
comparable with
magnitudes of external
forces
2) Operating speeds are high
Lo
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Balancing
Lecture 1
Dr J S Rathore
Objectives:
1. Rotating and Reciprocating unbalance
2. Importance of balancing in mechanical systems
3. Statically and Dynamically balanced (Completely balanced) system
4. Internal Balancing (S
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Introduction to Kinematics
Chapter1
J S Rathore
Terminology
Structure, mechanism and machine
Kinematic chain
Links
Kinematic pairs/joints
Four link planar mechanism/Slidercrank mechanism
Mobility and Degree of freedom : K
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Dynamics of Reciprocating Engine
Lecture1
J S Rathore
A four bar mechanism in the vertical plane is shown in Fig. The crank and follower, O2A and O4B, are of
equal lengths (80 cm) but of negligible mass. The coupler AB is a rigi
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Kinematics and
Dynamics
BITS Pilani
Pilani Campus
Sachin U Belgamwar
Instantaneous centre
(I centre)
The instantaneous centre , is the point in a body undergoing planar movement that
has zero velocity at a particular instant of time.
BITS Pilani, Pilani
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
Kinematics and
Dynamics
BITS Pilani
Pilani Campus
Radial CAM Nomenclature
BITS Pilani, Pilani Campus
Description of the follower
movement
1.
Rise movement of the follower away from the cam centre
2.
Dwell no movement of the follower
3.
Return movement
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Flywheel
Lecture 1
J S Rathore
Turning moment diagram (M):
sin 2
M P r sin
2 n 2 sin 2
M crank
CR M correction
 (1)
( pgas A mpiston a p mpiston g )
cos 2
2
a p r cos
n
M = Mgas + Minertia  (2)
M f (, )
4 Stroke I.
Birla Institute of Technology & Science, Pilani  Hyderabad
Kinematics and dynamics of machines
ME 242

Spring 2016
BITS Pilani
Pilani Campus
Crank 2 rotates with 2000 rpm
(CW).
EA=5 cm, AB=BC=15 cm,
CA= 5 cm, CD=12.5 cm
Find the accelerations of point B
and D.
BITS Pilani, Pilani Campus
OA rotates at 210 rpm in CCW increasing
at the rate of 60 rad/s2 .
(a) Velocity of