machine designing
TRANSCRIPT
KINEMATICS
OF MECHANISMS
ApplicationTo select drive and devices for power transmission. To operate and maintain machine and mechanism used in field of Automobile, machine tool, workshop etc.
Procedures Analysis of Mechanism in machine. Velocity and acceleration diagrams, cam profile……etc
Principles Conversion of Kinematic chain to mechanism, Relative Velocity and Acceleration in Mechanism, Law of Inversions and Governor.
Concepts
Mechanism, Inversion, Kinematic link, pair, Kinematic chain,constrain motion, velocity and acceleration in mechanism,displacement diagram, turning moment, torque, vibration,balancing.
Facts Cam, Follower, Belt, Chain, Gear, Flywheel, Governor, brake, clutch, Dynamometers
AIM
TO STUDY VARIOUS TYPES OF KINEMATIC LINKS,PAIRS,CHAINS,
MECHANISM,MACHINE AND STRUCTURE
KINEMATICS
RELEVANCE OF KINEMATIC STUDY
Motion requirements
Design requirements
MOTION STUDY
Study of position, displacement, velocity and acceleration of different elements of mechanism
Types of Motion
Pure rotation: the body possesses one point (center of rotation) that has no motion with respect to the “stationary” frame of reference. All other points move in circular arcs.
Pure translation: all points on the body describe parallel (curvilinear or rectilinear) paths.
Complex motion: a simultaneous combination of rotation and translation.
DESIGN REQUIREMENTSDesign: determination of shape and size
1. Requires knowledge of material
2. Requires knowledge of stress
Requires knowledge of load acting
(i) static load
(ii) dynamic/inertia load
WHAT DO YOU MEAN BY KINEMATIC LINK?
ORLINKOR
ELEMENT
Link:is a rigid body which possesses at lease two nodes which are points for attachment to other links.
nodes
Ternary link
Quaternary linkBinary link
nodes
Machine Element:
Binary link
This link has several machine elements
1. Cylinder 2. Piston 3. Coupler4. Crank5. Pinion6. Flywheel7. Gear8. Inlet cam9. Outlet cam10. Inlet valve11. Outlet valve
Examples of rigid links
EXAMPLE:
SLIDER CRANK MECHANISM CONSIST OF FOUR LINKS:
•FRAME AND GUIDES
• CRANK
•CONNESTING ROD
•SLIDER
SLIDER CRANK MECHANISM:
CONSTRAINED MOTION
One element has got only one definite motion relative to the other
(a) Completely constrained motion
(b) Successfully constrained motion
(c) Incompletely constrained motion
KINEMATIC PAIR
AND CLASSIFICTIO
N
PAIRING ELEMENTS
PAIRING ELEMENTS
KINEMATIC PAIRS ACCORDING TO NATURE OF CONTACT:
LOWER PAIR:LINKS HAVING SURFACE OR AREA
CONTACT
EXAMPLE:I)NUT TURNING ON A SCREW2)SHAFT ROTATING IN A BEARING
1 2
Turning pair
Link 2(guide, slot)
Link 1(slider)
sliding pair
Lower pairs
Prismatic joint Revolute joint Cylindric joint Spherical joint Helical joint Planar joint
Type P joint R joint C joint S joint H joint F joint
DOF 1 1 2 3 1 3
HIGHER PAIR(POINT OR LINE CONTACT BETWEEN LINKS)
EXAMPLE:
• WHEN ROLLLING ON A SURFACE
• CAM AND FOLLOWER
• TOOTHED GEARS
• BALL AND ROLLER BEARINGS
HIGHER PAIRS:
Examples of higher pairsHigher pairs
1 (cam)
2 (follower)
DOF
5 2
Examples of higher pairsHigher pairs
1 (cam)
2 (follower)
KINEMATIC PAIRS ACCORDING TO THE NATURE OF RELATIVE
MOTION:
REVOLUTE PAIR:
PRISMATIC PAIR:
SCREW PAIR:
CYLINDRICAL PAIR:
SPHERICAL PAIR:
PLANAR PAIR:
KINEMATIC PAIRS ACCORDING TO MECHANICAL CONSTRAINT:
CLOSED PAIR: (WHEN THE ELEMENTS OF PAIR ARE
HELD TOGETHER MECHANICALLY)
EXAMPLE ALL THE LOWER PAIRS AND SOME OF
THE HIGHER PAIR
UNCLOSED PAIR: (WHEN TWO LINKS OF PAIR ARE IN
CONTACT EITHER DUE TO FORCE OF GRAVITY OR SOME SPRING ACTION)
EXAMPLECAM AND FOLLOWER
KINEMATIC CHAIN
LOCKED CHAIN OR STRUCTURE
Links connected in such a way that no relative motion is possible.
MECHANISM
Slider crank and four bar mechanisms
Working of slider crank mechanism
Unconstrained kinematic chain
PLANAR MECHANISMSWhen all the links of a mechanism have plane motion, it
is called as a planar mechanism. All the links in a planar mechanism move in planes parallel to the reference plane.
TYPES OF KINEMATIC CHAIN:
• FOUR BAR CHAIN MECHANISM
• SINGLE SLIDER CRANK CHAIN
• DOUBLE SLIDER CRANK CHAIN
MACHINE AND
STRUCTURE
Characteristics of a machine:
1. Composed of man-made elements
2. The elements are arranged to transmit motion
3. Can transmit energy, and fulfill certain work for human being.
Degrees of freedom ormobility of a mechanism
It is the number of inputs (number of independent coordinates) required to describe the configuration or position of all the links of the mechanism, with respect to the fixed link at any given instant.
51
Degrees of Freedom (DOF) or Mobility
• DOF: Number of independent parameters (measurements) needed to uniquely define position of a system in space at any instant of time.
Rigid body in a plane has 3 DOF: x,y,
Rigid body in space has 6 DOF (3 translations & 3 rotations)
GRUBLER’S CRITERIONNumber of degrees of freedom of a
mechanism is given by F = 3(n-1)-2l-h. Where,F = Degrees of freedomn = Number of links in the mechanism.l = Number of lower pairs, which is obtained
by counting the number of joints. If more than two links are joined together at any point, then, one additional lower pair is to be considered for every additional link.
h = Number of higher pairs
Examples - DOF
F = 3(n-1)-2l-hHere, n = 4, l = 4 & h = 0.F = 3(4-1)-2(4) = 1I.e., one input to any one link will
result in definite motion of all the links.
Grubler's Equation
A rigid body is constrained by a lower pair, which allows only rotational or sliding movement. It has one degree of freedom, and the two degrees of freedom are lost.
When a rigid body is constrained by a higher pair, it has two degrees of freedom: translating along the curved surface and turning about the instantaneous contact point.
N - number of kinematic elements including the fixed member.
L - number of lower pairs in the mechanism
H - the number of higher pairs in the mechanism
Then, the resultant number of degrees of freedom in the mechanism (this should be one)
F = 3(N-1) - 2L – H = 1,
which gives
3N - 2L - H = 4
This is known as Grubler’s Equation.
F = 3(n-1)-2l-hHere, n = 5, l = 5 and h = 0.F = 3(5-1)-2(5) = 2I.e., two inputs to any two links are
required to yield definite motions in all the links.
F = 3(n-1)-2l-hHere, n = 6, l = 7 and h = 0.F = 3(6-1)-2(7) = 1I.e., one input to any one link will result in definite motion of all the links.
F = 3(n-1)-2l-hHere, n = 6, l = 7 (at the intersection of 2, 3 and 4, two
lower pairs are to be considered) and h = 0.F = 3(6-1)-2(7) = 1
F = 3(n-1)-2l-hHere, n = 11, l = 15 (two lower pairs at the intersection
of 3, 4, 6; 2, 4, 5; 5, 7, 8; 8, 10, 11) and h = 0.F = 3(11-1)-2(15) = 0
(a)F = 3(n-1)-2l-hHere, n = 4, l = 5 and h = 0.F = 3(4-1)-2(5) = -1I.e., it is a structure
(b) F = 3(n-1)-2l-hHere, n = 3, l = 2 and h = 1.F = 3(3-1)-2(2)-1 = 1
(c) F = 3(n-1)-2l-hHere, n = 3, l = 2 and h = 1.F = 3(3-1)-2(2)-1 = 1
INVERSIONS OF MECHANISM
A mechanism is one in which one of the links of a kinematic chain is fixed. Different mechanisms can be obtained by fixing different links of the same kinematic chain. These are called as inversions of the mechanism.
Where would you see 4-bar mechanisms?
Grashof condition predicts behavior of linkage based only on length of links S=length of shortest link L=length of longest link P,Q=length of two remaining links
If S+L ≤ P+Q the linkage is Grashof :at least one link is capable of making a complete revolution
Otherwise the linkage is non-Grashof : no link is capable of making a complete revolution
The Grashof Condition
For S+L<P+QCrank-rocker if either
link adjacent to shortest is grounded
Double crank if shortest link is grounded
Double rocker if link opposite to shortest is grounded
For S+L>P+Q All inversions will be double rockers
No link can fully rotate
69
For S+L=P+Q (Special case Grashof)
• All inversions will be double cranks or crank rockers
• Linkage can form parallelogram or antiparallelogram
• Often used to keep coupler parallel (drafting machine)
Parallelogram form
Anti parallelogram form
Deltoid form
70
Linkages of more than 4 bars
5-bar 2DOFGeared 5-bar 1DOF
• Provide more complex motion• See Watt’s sixbar and Stephenson’s sixbar
mechanisms in the textbook
Linkages of more than 4 bars
72
More Examples: Front End Loader
73
Drum Brake
EXAMPLE FOR SUPERSTRUCTURE
(link 1) frame(link 2) crank(link 3) coupler (link 4) rocker
Four bar mechanism
1
2
3
4
1
(1:2), (2:3), (3:4), (4:1) - Turning pairs
Link 1 is fixed
INVERSIONS OF FOUR BAR CHAIN
1. Double Crank mechanism: parallel 4 bar linkage which is used in coupled wheels of locomotive)
1. Beam engine (crank- rocker mechanism)
1. Watts indicator diagram (Rocker-rocker)
DOUBLE CRANK MECHANISM
PARALLEL-4 BAR LINKAGE MECHANISM
CRANK-ROCKER MECHANISMDRAG LINK MECHANISM
CRANK-ROCKER MECHANISM
INVERSIONS OF SLIDER CRANK CHAIN
Inversions of Slider-crank Mechanism
Slider crank mechanism (link-1 is fixed)
Main bearing 1(fixed)
Crank 2Connecting rod 3
Piston 4
Cylinder 1 (fixed)
IDC ODC
Stroke length (L=2r)
r
LINK1 IS FIXED
SLOT
CRANK
APPLICATION:RECIPROCATING PUMPS,RECIPROCATINGCOMPRESSORS,OSCILLATING CYLINDER ENGINE
PISTON
CRANK SHAFT
1
23
4
Link 2 is fixed
12
3 4 Inversion 2 (link-2 is fixed)
Whitworth quick-return mechanism or Gnome aircraft engine
Whitworth quick return motion mechanism
APPLICATION:SHAPING AND SLOTTING MACHINE
1
2 3
4
Link 3 is fixed
Inversion 3 (link-3 is fixed)
The oscillating cylinder engine Foot pump
1
2
3
4
Crank and slotted lever quick return motion mechanism
Crank and slotted lever quick return motion mechanism
Application of Crank and slotted lever quick return motion mechanism
1
2
3
4
Inversion 4 (link- 4 is fixed)
Hand-pump
Oscillating cylinder mechanism (connecting rod fixed)
APPLICATION:HAND PUMP
Pendulum pump or bull engine–inversion of slider crank mechanism (slider fixed)
– A simple example (simple crank – slider mechanism)• The structure
• The mathematical model r
l
u
l+r
l-r
x
Rotary engine– (crank fixed)
DOUBLE SLIDER CRANK CHAIN
It is a kinematic chain consisting of two turning pairs and two sliding pairs.
SCOTCH –YOKE MECHANISMTurning pairs –1&2, 2&3; Sliding pairs – 3&4, 4&1
SCOTCH-YOKE MECHANISM
4
1
32
A
B
ELLIPTICAL TRAMMEL
ELLIPTICAL TRAMMEL
11
1
2
4
OLDHAM COUPLING
OLDHAM COUPLING
Quick return motion mechanisms
Drag link mechanism
Whitworth quick return motion mechanism
Crank and slotted lever quick return motion mechanism
DRAG LINK MECHANISM
12
21
ˆ
ˆ
BAB
BAB
urnstrokeTimeforret
wardstrokeTimeforfor
INTERMITTENT MOTION MECHANISMS
Ratchet and pawl mechanism
APPLICATION:CLOCKS AND WATCHES, FEED MECHANISMS,LIFTING JACK
AND COUNTING DEVICES
Application of Ratchet Pawl mechanism
Geneva wheel mechanism
APPLICATION:CLOCKS AND WATCHES,FEEDING OF FIM ROLL IN EARLY MOTION PICTURE
TOGGLE MECHANISM
TOGGLE MECHANISM
APPLICATION:TOGGLE CLAMPS,RIVETTING M/C,SHEET METALPUNCHING,
FORMING, PRESS,STONE CRUSHERS,SWITCHES,CIRCUIT BREAKERS,
Straight line motion mechanisms
..,
.
constACifABconstAE
constbutADAD
ACABAE
AE
AB
AC
AD
ABDAEC
Locus of pt.C will be a straight line, ┴ to AE if, AB*AC
is constant.
Proof:
Peaucellier mechanism
FIG1
SCOTT RUSSEL MECHANISM
PANTOGRAPH
Hooke’s joint
STEERING GEAR MECHANISM
Ackermann steering gear mechanism
CL
SL
Ackermann steering gear mechanism
TEN BAR STEERING
14 BAR STEERING