Presentation
by
SURESH KUMAR S
B.E, M.E (Machine Design)
Asst.Professor, Dept. of Mechanical Engg.
ATME Mysore
Mob:9739582217
Chapter-1
Introduction
 Introduction: Definitions Link or element, kinematic pairs,
Kinematic chain
 Mechanism, Structure, Mobility of Mechanism, Inversion,
Machine
 Degrees of freedom, Grubler's criterion (without
derivation)
 Kinematic Chains and Inversions: Inversions of Four bar
chain; Single slider crank chain and Double slider crank
chain.
Kinematics
Kinematics: It is the branch of machine
which deals with the relative motion
between the various parts of the machine.
Why Kinematic Analysis of mechanism?
Determine appropriate movements
Determine an assembly
mechanism components
configuration
of
Subsequent analysis of the component motions
(kinematics) for proper all-around operation of the
mechanism
Mechanism in a Excavator
Element or Link
Each part of a machine which has motion relative to some
other parts is termed an element or link
A link need not necessarily be rigid body, but it must be a
resistant body
E.g: crank shaft, connecting rod
Different shapes Links
Kinematic Pair
When two elements or links are connected together in such a way
that their relative motion is constrained, form a Kinematic pair
If the constraint is not complete the pair is termed as incomplete
or unsuccessful
Classification of Kinematic pair
Kinematic pairs may be classified as higher and lower pairs
Higher pair are the ones consisting of line or point contact
while in motion as in the case of a roller or ball bearing
Lower pair are the ones consisting of surface contact
between two links as in pin joint or a slider
These may be classified as turning pairs, sliding pairs,
spherical pairs, screw or helical pairs and rolling pairs
Kinematic Pairs
• Sliding Pair – Two elements are so connected
that one is constrained to have a sliding
motion relative to the other
Turing Pair – when two element are so connected
that one is constrained to turn about a fixed axis of
other it forms a turning pair
E.g.. Crank Shaft turning in a bearing
Screw Pair – When one element turns about the
other element by means of threads, it forms a screw
or helical pair
E.g.. Bolt and nut
Spherical Pair- when one element is in the form of
sphere turns about the other fixed element it forms
a spherical pair
E.g.. Ball and Socket joint
Rolling Pair – when two elements are so
connected that one is constrained to roll in
other fixed element it forms a rolling pair
E.g.. Ball and roller bearing
Kinematic pairs
Kinematic Chain
A kinematic chain is any group of links connected together
for the purpose of transmitting forces or motions
Locked Kinematic chain is an arrangement of links such that
no link can move relative to the other links in the chain
Constrained Kinematic Chain is an arrangement of links such
that a movement of one link causes a definite predictable
movement of the other links
Unconstrained Kinematic Chain is an arrangement of links
such that a movement of one link does not cause a
predictable movement of the other links
Mechanism
• A mechanism is a constrained kinematic chain.
With one link fixed and is used to transmit or
transform motion
Inversion
•
By making a different link in a kinematic chain
the fixed member, we obtain a different
mechanism. Thus any one of the links may be
arbitrarily selected as the fixed link, and each
arrangement is an inversion of the others
Machine
A machine is a mechanism or group of
mechanism used to perform useful work. Its chief
function is to adopt a source of power to some
specific work requirement
Quadratic Chain
Quadratic chain is a four links kinematic chain
Four bar chain and its inversion
A four bar mechanism is a mechanism having four rigid links with
one link fixed, the chain consists of four turning pairs
The fixed link is referred to as the frame
The rotating link is called the driver or crank
The other rotating link is called the follower or rocker
The floating link is called the connecting rod
Four bar chain
Four bar chain
Four bar chain
Four bar chain inversions
1.Beam engine or crank and lever mechanisms
2.Coupling Rod of a Locomotive
3. Watt indicator mechanisms
Beam Engine(oil well pump)
Coupling Rod of a Locomotive
This is an example of a double crank mechanism where
both cranks rotate about the fixed centers A and B as
shown in Fig
In this mechanism the opposite links are equal in
length, that is
AB = CD and AD = BC. Link AB is fixed
3. Watt indicator mechanisms
Watt’s Indicator
Single Slider Crank Chain
• A slider crank is a special case of the four bar mechanism
having three turning pairs and one sliding pair
• The simplest form is the reciprocating engine mechanism as
shown. The slotted link AB is fixed. As the crank BC rotates,
the die block D reciprocates
Single slider mechanism
Single slider mechanism
Single slider Inversions
1.Pendulum pump
2. Oscillating cylinder engine
3.Rotary internal combustion engine
Oscillating Cylinder Engine
• Inversion is obtained by fixing the link CD as shown in fig
• As the crank rotates about C the slotted link AB slides over the
die block which is pivoted to the fixed link at D
• The mechanism of oscillating cylinder engine is based upon it
3.Rotary Internal combustion or gnome engine
Double Slider Crank Chain and its Inversions
• The kinematic chain consists of two turning and two sliding
pair
• Two slide block A and B slide along slots in a frame S and the
pins A and B on the slide blocks are connected by the link AB
as shown
• Such a Kinematic chain has three inversions
• 1. Elliptical Trammel
• 2. Oldham’s Coupling
• 3. Scotch Yoke Mechanism
Elliptical Trammel
•
It is an instrument for drawing ellipses. The slotted frame
S is fixed. Any point, such as P on the link AB except the
midpoint of AB will trace an ellipse as the slide blocks A
and B slide along their respective slots
The equation of an ellipse with centre at O is given by
sin2θ + cos2θ = x2 / a2 + y2/ b2 = 1
Elliptical Trammel
Oldham’s Coupling
• Second inversion is obtained by fixing the link AB
as shown
• For a given angular displacement of any one of
the slide block, the frame and other block will turn
through the same angular displacement
Scotch Yoke Mechanism
• Third inversion is obtained by fixing any one of
the two blocks A or B as shown in fig
• The link AB can rotate about A as centre and thus
cause the frame to reciprocate
Scotch Yoke Mechanism
Chapter2-MECHANISMS
Crank and slotted lever quick return motion
mechanism
Shaper Mechanisms
Whitworth Quick Return Mechanism
• The inversion is obtained by fixing the link BC. It is
used in a number of applications such as slotting
and shaping machines
• The crank CD rotates at uniform speed. The die
block D slides along the slotted link AB and causes
this to revolute about B with variable speed
Whitworth Quick Return
Mechanism
Straight line motion mechanisms
1. Peaucellier mechanism
1. Peaucellier mechanism
2.Roberts Mechanisms
Intermittent motion mechanisms
1. Geneva Mechanisms
2.Ratchet and pawl Mechanisms
2.Ratchet and pawl Mechanisms
Degrees 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 rigid body can be moved
Degrees of freedom of a rigid body in a plane
Steering gear mechanism
Ackerman Steering gear mechanism
Degrees of Freedom
a.
b.
c.
A rigid body is constrained by a revolute pair which
allows only rotational movement around an axis
a rigid body is constrained by a prismatic pair which
allows only translational motion
It has two degrees of freedom: translating along the
curved surface and turning about the instantaneous
contact point
Kutzbatch’s Equation
• Kutzbach modified Gruebler’s equation and it
is given by
M = 3 (L – 1) – 2J1 – J2
Where: M = degree of freedom or mobility
L = number of link
J1 = number of 1 DOF
J2 = number of 2 DOF
Grashof Condition
• In a Four bar Mechanism let the length of the shortest
and longest links be denoted by S and L, respectively.
The intermediate links will be labeled P and Q.
• If we compare the quantity S+L with P+Q, we can get
a tell if any of the links will be able to rotate or not.
• The Grashof condition states that if:
• S+L≤P+Q then the mechanism is a Grashof mechanism
and at least one link will be capable of a full
revolution.
• If S+L>P+Q then the mechanism is nonGrashof and all combinations of the links
will be double rockers and none of the links
will be capable of a full rotation.
Special case Grashof
If S+L=P+Q then we have a special case Grashof and the mechanism will
have changeovers where it can switch configurations and the output can
be indeterminate.
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