3. A Machine-
• Minimize human efforts, and energy
• Saves time
• Convert one form of energy into another form.
• Has moving parts
• Does useful work
Prof A B Karpe
5. UNIT 1
• Fundamentals of Kinematics and Mechanisms
Mechanics
Dynamics
(Involves force
& their effects)
Kinetics
(Study of inertia
forces when body is in
motion)
Kinematics
(Study from geometric
point of view)
(Relative motion bet
various parts)
Statics
(Study of forces
when the body is
stationary)
Prof A B Karpe
6. Can you find the difference?
CAR BRIDGE
Prof A B Karpe
7. Machine Structure
The parts of a machine move
relative to one another
The members of a structure
do not move relative to one
another
A machine transforms the
available energy into some
useful work
a structure no energy is
transformed into useful work
The links of a machine may
transmit both power and
motion
the members of a structure
transmit forces only
Drilling machine, lathe
machine etc
A railway bridge, a roof
truss, machine frames etcProf A B Karpe
8. Kinematic Link or Element
• Each part of a machine, which moves relative
to some other part, is known as a kinematic
link (or simply link) or element.
Prof A B Karpe
9. Types of links
• Rigid link- Piston, Connecting Rod, crank etc.
• Flexible link- belts, ropes, chains and wires etc.
• Fluid Link- Hydraulic presses, jacks and brakes
etc
Prof A B Karpe
12. Classification of Kinematic Pairs
A. According to the type of relative motion between
the elements
1) Sliding pair- The piston and cylinder, cross-head and guides of a
reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe
bed etc
2) Turning pair- A shaft with collars at both ends fitted into a circular hole,
the crankshaft in a journal bearing in an engine, lathe spindle supported in head
stock, cycle wheels turning over their axles etc
3) Rolling pair- Ball and roller bearings
4) Screw pair- lead screw of a lathe with nut, and bolt with a nut
5) Spherical -ball and socket joint, attachment of a car mirror, pen stand
Prof A B Karpe
15. B. According to the type of contact between the
elements
1) Higher pair-Point or line contact- A pair of friction discs, toothed
gearing, belt and rope drives, ball and roller bearings and cam and
follower
2) Lower pair- surface contact- sliding pairs, turning pairs and screw
pairs form lower pairs
Prof A B Karpe
16. C. According to the type of closure
i. Self closed pair
ii. Force - closed pair
Prof A B Karpe
17. Kinematic chain
• When the kinematic pairs are coupled in such a way
that the last link is joined to the first link to transmit
definite motion (i.e. completely or successfully
constrained motion), it is called a kinematic chain
unconstrained chain
Prof A B Karpe
18. Type of joints in a kinematic chain
• Binary
• Ternary
• Quaternary
J = 3x(no. of quaternary)+2x(no. of ternary)+no. binary
Prof A B Karpe
19. Classification of Links
• Binary link - one with two nodes.
• Ternary link - one with three nodes.
• Quaternary link - one with four nodes.
• Node: where another link can be connected
with pin joint
Prof A B Karpe
20. Mechanism
• When one of the links of a kinematic chain is fixed the chain is
known as Mechanism.
• It may use to transmitting or transforming motion eg. Slider-crank
mechanism, typewriter etc
• Simple mechanism- four links
• Compound Mechanism – more than four links.
Prof A B Karpe
21. Machine Mechanism
The machine is a device to which energy is
supplied in any form and the output is
obtained in the form of useful mechanical
work.
Mechanism is a kinematic
chain in which one link is fixed.
Machine can be a combination of number of
mechanisms.
Mechanism is a combination
of number of kinematic links.
Machine is designed for transmitting motion
as well as forces.
By and large mechanism is
designed for transmitting motions.
While designing the machine physical
parameters like stress, temperature
etc. are considered.
While designing a mechanism
generally lengthwise
dimensions are considered.
Examples : Lathe, milling, drilling, shaping,
slotting, machines etc.
Examples : Typewriter,
clock mechanisms etc.Prof A B Karpe
22. Grashoff’s Law
L1 length of Link 1(frame)
L2 length of Link 2(crank)
L3 length of link 3(coupler)
L4 length of link 4(rocker)
Its is necessary that one link must be the revolving link.
L4 + L3 <= L1 + L2
For a planer for bar linkage, the sum of the shortest and
the longest link length cannot be greater than sum of the
remaining two link length, if there is a continuous relative
motion between the two members.
Prof A B Karpe
24. Degree Of Freedom
• The degrees of freedom (DOF) of a rigid body is defined as the
number of independent movements it has. To determine the DOF
of this body we must consider how many distinct ways the bar can
be moved.
Prof A B Karpe
27. n= No. of degree of Freedom
L= No. of Links
j= No. Joints
h= Higher Pairs
Prof A B Karpe
28. Application of Kutzbach Criterion
(a) When n = 0, then the mechanism forms a structure and no relative motion between the links is possible, as
shown in Fig. (a) and (d).
(b) When n = 1, then the mechanism can be driven by a single input motion, as shown in Fig. (b).
(c) When n = 2, then two separate input motions are necessary to produce constrained motion for the
mechanism, as shown in Fig. (c).
(d) When n = – 1 or less, then there are redundant constraints in the chain and it forms a statically
indeterminate structure, as shown in Fig. (e). Prof A B Karpe
29. Here it has been assumed that the slipping is
possible between the links
Prof A B Karpe
30. Grubler’s Criterion
Applied to 1 DOF mechanisms only
Mechanism of 1 DOF cannot have odd number of
links. e.g. four bar chain, single slider mechanism
four bar mechanism and a slider-crank mechanism in which l = 4 and j = 4.
Prof A B Karpe
31. Fig. shows schematic of a mechanism. Redraw the free-hand sketch on the answer book. Find out
the total number of kinematic links and number of kinematic pairs. Hence find out the degrees of
freedom for the mechanism
[4 MARKS]
Prof A B Karpe
32. Problem -1
Fig. shows schematic of a
mechanism. Redraw the free-
hand sketch on the answer book.
Find out the total number of
kinematic links and number of
kinematic pairs. Hence find out
the degrees of freedom for the
mechanism
[4 MARKS]
l=8, j=10, h=0---- n=1
Prof A B Karpe
33. Problem -02
• Fig. shows schematic of a
mechanism. Redraw the free-
hand sketch on the answer
book. Find out the total
number of kinematic links and
number of kinematic pairs.
Hence find out the degrees of
freedom for the mechanism.
[4]
l=8, j=10, h=0---- n=1
Prof A B Karpe
34. Problem -03
Figure shows schematic of
a mechanism. Redraw the
free hand sketch on the
answer-book. Find out the
total number of kinematic
links and number of
kinematic pairs. Hence
find out degrees of
freedom for the
mechanism. [
l=9, j=11, h=0---- n=2
Prof A B Karpe
35. PROBLEM M-04
Figure shows schematic of a
mechanism. Redraw the free
hand sketch on the answer-
book. Find out the total
number of kinematic links
and number of pairs. Hence
find out degrees of freedom
for the mechanism. [4]
l=9, j=11, h=0---- n=2
Prof A B Karpe
36. Problem -05
• Justify the linkages shown
in Fig. is a mechanism with
single degree of freedom.
L=5, j=5, h=1---- n=1
Prof A B Karpe
37. Problem -06
• Define degrees of freedom of a mechanism
and find degrees of freedom for the following
cases (Fig. 1 and Fig. 2). [8 MARKS]
L=8, j=10, h=0---- n= L=3, j=2, h=1---- n=1
Prof A B Karpe
40. Basic Kinematic Chain
• Four Bar Chain or Mechanism
• Single Slider Crank Mechanism
• Double Slider Crank Mechanism
Prof A B Karpe
41. Inversion of mechanism
• Obtain as many mechanisms as the number of
links in a kinematic chain by fixing, in turn,
different links in a kinematic chain. This
method of obtaining different mechanisms by
fixing different links in a kinematic chain is
known as inversion of the mechanism.
Prof A B Karpe
42. Types of Inversions
Types of Kinematic Chains
Four bar chain or
quadric cyclic chain
Single slider crank
chain
Double slider crank
chain
1. Beam Engine
2. Coupling rod of a
locomotive
3. Watt’s indicator
1. Pendulum pump
2. Oscillating cylinder engine
3. Rotary internal combustion
engine or Gnome engine
4. Whitworth quick return
motion mechanism
5. Crank and slotted lever quick
return motion mechanism
1. Elliptical
trammels
2. Scotch yoke
mechanism
3. Oldham 's
coupling
Prof A B Karpe
43. Inversions Of Four Bar Mechanism
• Four bar chain is the simplest and basic kinematic chain . It consists of four
link A,B,C,D . The length of four links may be different. In four bar chain ,
the shortest link will make complete revolution relative to the other three
links.
• This link is call as driver or crank (link AB or link 2).
• The link which connected the crank and lever is called coupler (link BC link
3).
• The link which makes partial rotation or oscillation is called as lever or
rocker (link CD or link 4).
• The fixed link of the mechanism is called frame (link AD or link 1).
Prof A B Karpe
44. Four bar chain or quadric cyclic chain
• Beam Engine Mechanism
is the most popular
example of crank and lever
mechanism. The purpose
of this mechanism is to
convert rotary motion into
reciprocating motion.
Prof A B Karpe
46. Coupling rod of a locomotive
•This mechanism is
meant for transmitting
rotary motion from one
wheel to the other wheel.
•Coupled wheels of
locomotive is the
example of double crank
mechanism.
Prof A B Karpe
47. Watt’s indicator
also known as Watt's straight line mechanism or double lever mechanism)
The displacement of the link BFD is directly proportional to the pressure of gas or steam
which acts on the indicator plunger Prof A B Karpe
48. Inversions Of Single Slider Crank Chain Mechanisms
Single slider crank chain is a modification of four bar chain
mechanism. It consists of one sliding pair and three turning pair. This
mechanism is used to converts rotary motion into reciprocating
motion.
• Ex. Reciprocating steam engine mechanism
Prof A B Karpe
53. Crank and Slotted Lever quick return
motion
This mechanism is mostly used in shaping machines and slotting machines and
rotary internal combustion engine.
Prof A B Karpe
57. Double slider crank chain
A kinematic chain which consists of two turning pairs and two sliding pairs is
known as double slider crank chain
Elliptical trammel useful for tracing the elliptical curves.
Prof A B Karpe
58. Scotch yoke mechanism
This mechanism is used for converting rotary motion into a reciprocating motion
Prof A B Karpe
60. Pantograph
A pantograph is an instrument used to reproduce to an enlarged or a
reduced scale and as exactly as possible the path described by a given
point.
1.It is most widely used for reproduction of plane areas and geometrical
figure s like maps, plans , drawing etc. on enlarge or reduce the scale.
2.It is used as an indicator rig to reproduce the displacement of the corss-
head and hence the piston of a reciprocating steam engine.
3.Pantograph is also used to guide the cutting tools.
4.A modified form of pantograph is used to collect power at the top of an
electric locomotive.
Prof A B Karpe
61. STRAIGHT LINE MECHANISM
1.Exact straight line mechanism
a) Peaucellier mechanism
b) Hart’s mechanism
c) Scoot Russel mechanism
2.Approximate straight line mechanism
a) Grass Hopper’s mechanism
b) Watt’s mechanism
c) Robert’s mechanism
Prof A B Karpe
71. Steering Gear Mechanisms
• front wheels are mounted on short axles called stub axles.
• Back wheels are mounted on rear axle at two ends of the differential.
Prof A B Karpe
73. Condition for correct steering
For pure rolling motion , the two
front wheels must turn about the
same Instantaneous centre I which
lies on the axis of back wheel as
shown figure.
The axis of inner wheels makes a
larger angle θ than the angle ф
turned by the outer wheels
Prof A B Karpe
74. From
In Δ IBD ,
In Δ IAC ,
(1)
Above eq (1) represents the fundamental equation for correct
steering. If this condition is satisfied then the motion of wheel
will of pure rolling and no skidding will take place.
The mechanisms used for automatically adjusting the values
of θ and ф for correct steering are called steering gears.
Prof A B Karpe
75. TYPES OF STEERING GEARS
There are two main types of steering gears
1. Ackermann steering gear
An Ackermann steering gear has only turning pairs and thus is
preferred. Its drawback is that it fulfils the fundamental
equation of correct gearing at the middle and the two
extreme positions and not in all positions.
2. Davis steering gear
A Davis steering gear has sliding pairs which means more
friction and easy wearing. The gear fulfils the fundamental
equation of gearing in all the positions. However, due to
easy wearing it becomes inaccurate after some time.
Prof A B Karpe
76. Types Of Steering Gears
Davis steering gearAckermann steering gear Prof A B Karpe
81. Limitation of Davis steering gear mechanism
1.In this mechanism due to presence of few sliding pairs, friction is
high and wear at contact surface is high. This result in decrement in
the accuracy of the mechanism.
2.Hence, through this mechanism gives correct steering, they are
not in common used.
Prof A B Karpe
82. Bell Crank Lever Linkage
Additional Images
Rack and Pinion Linkage
Prof A B Karpe
83. Davis Steering Gear
1. It consists of two
turning and two sliding
pairs.
2. This is an exact steering
gear mechanism.
3..The mechanism lies
front side of front
wheels.
4.Due to presence of
sliding pairs ,the friction
is more and they wear
out rapidly.
Ackermann steering Gear
1 It consists of four turning
pairs.
2. This is an approximate
steering gear mechanism.
3.The mechanism lies back
side of front wheels.
4.Due to non sliding pair
friction is less and hence
wear is less.
Prof A B Karpe
84. Equivalent Linkage
• Many times the physical shape of connection between the links is such that actual
nature and function of connections are not notified directly. And that is because
the centre of revolute pair is not directly apparent. Therefore a mechanism with
higher pair can be replaced by an equivalent mechanism with lower pair. This
equivalence is valid for studying only the instantaneous characteristics.
• One higher pair is converted to two lower pairs by placing one binary link.(normal
to contacting surfaces)
Prof A B Karpe
