Introduction to Theory of Machines and its Kinetics,Kinematic chains and their inversions

1. CH.1.
FUNDAMENTALS AND TYPES OF
MECHANISMS
By Pooja Katkar
Lecturer
(Pimpri Chinchwad Polytechnic,Pune)

2. Theory Of Machines
• Branch of Engineering Science which deals
with study of relative motion between various
parts of a machine
2By Pooja Katkar

3. Divisions of Mechanics
Mechanics
Deals with study of
motions
Dynamics
Deals with systems
which change with
time
Kinetics
Deals with Motion
and Time
Kinematics
Deals with Motion,
Time and Forces.
Statics
Deals with systems
which don’t change
with time
3By Pooja Katkar

4. Statics Kinematics Kinetics
STRUCTURE MECHANISM MACHINE
• Machine – device to transfer or transform energy to
do useful work.
• Mechanism – device to transfer or transform given
input motion to specified output motion
• Structure – a single body with no motion /
combination of bodies with no relative motion
4By Pooja Katkar

5. 5By Pooja Katkar

6. 6By Pooja Katkar

7. Components of Mechanisms
• Link / element
• Kinematic pairs / joints
• Kinematic chain
7By Pooja Katkar

8. 8By Pooja Katkar

9. LINK
• Part of machine which moves relative to other part
• Rigid Body Flexible Body Liquid
9By Pooja Katkar

10. KINEMATIC PAIR
• Combination of two links kept in permanent contact
with each other
• relative motion(s) between them is constrained or
unconstrained
10By Pooja Katkar

11. 11By Pooja Katkar

12. BASED ON THE RELATIVE MOTION
• Sliding pair
• Rolling pair
• Turning pair
• Screw pair
• Spherical pair
12By Pooja Katkar

13. Classification of Pairs
• BASED ON NATURE OF CONTACT BETWEEN LINKS:
1. Lower Pairs -- Surface Contact
2. Higher Pairs – Point or Line Contact
13By Pooja Katkar

14. BASED ON HOW THE CONTACT IS MAINTAINED:
1. Self / Form Closed Pairs – Shape/Form of the links
maintain the contact. No external force.
2. Force Closed Pairs – External forces like gravitational force,
spring force etc., required to maintain the contact.
14By Pooja Katkar

15. Kinematic Chain
Assembly of links and pairs to produce required
/ specified output motion(s) for given input
motion(s)
15By Pooja Katkar

16. Mechanism
A kinematic chain with one fixed / stationary
link.
16By Pooja Katkar

17. Mechanism
• Driver :
Part of mechanism which
moves initially w.r.t. frame
/fixed link
• Follower :
Part of mechanism to which
motion is transmitted
17
Kinematic
chain
One link
fixed
Mechanism
By Pooja Katkar

18. • 2
18By Pooja Katkar

19. Kinematic Inversions
• Process of obtaining different mechanisms from the
same kinematic chain, by fixing different links in turn,
is known as kinematic inversion.
• Inversion of the kinematic chain depends upon which
link is fixed.
19By Pooja Katkar

20. Types of Kinematic Chains
• Kinematics with 4 lower pairs are in
consideration & all pairs are sliding or
turning pair
1. Four Bar Chain /Quadric Cycle Chain
2. Single Slider Crank
3. Double Slider Chain
20By Pooja Katkar

21. Grashoff’s Law
• Lengths of links: Longest link - l
Shortest link - s
Intermediate links – p, q
• Atleast one link will have full rotation if
• l + s ≤ p + q
21By Pooja Katkar

22. Important Kinematic Chains
 consist of four lower pairs
 All pairs are sliding pair or a turning pair.
 kinematic chains important from the subject point
of view :
1. Four bar chain or quadric cyclic chain
2. Single slider crank chain
3. Double slider crank chain
22By Pooja Katkar

23. Four Bar Chain /Quadric Cycle Chain
•crank or driver - the shortest
link makes a complete
revolution relative to the other
three links
•lever or rocker or follower -
makes a partial rotation or
oscillates
•connecting rod or coupler -
connects the crank and lever
•Frame - fixed link
23
In each inversion , the shortest link s is adjacent to the longest link l
By Pooja Katkar

24. INVERSIONS OF Four Bar Chain
• drag-link mechanism -fixing the shortest link s as the
frame,both links adjacent to s can rotate continously, and
both are properly described as cranks: the shortest used as
the input
• crank-rocker mechanism - shortest links is adjacent to the
fixed link Link s, the crank, since it is able to rotate
continously , and link p, which can only oscilate between
limits, is the rocker.
• double-rocker mechanism - fixing the link opposite to s
,although link s is able to make a complete revolution ,
neither link adjacent to the frame can do so; both must
oscilate between limits and are therefore rockers.
• parallelogram or change-point or crossover-position
mechanism - s=p and l=q
24By Pooja Katkar

25. 25By Pooja Katkar

26. FBC-Inversion 1-(Crank Rocker) BEAM
ENGINE
26By Pooja Katkar

27. FBC-Inversion 1-(Crank Rocker) BEAM
ENGINE
• purpose of this mechanism is
to convert rotary motion into
reciprocating motion.
• crank rotates about fixed
centre A
• lever = CDE ; oscillates about
fixed centre D
• end E of is connected to a
piston rod
• Piston rod reciprocates due
to the rotation of the crank.
27By Pooja Katkar

28. FBC-Inversion 2- (Double Lever
Mechanism) PANTOGRAPH
28By Pooja Katkar

29. 29By Pooja Katkar

30. Pantographs
• bends to allow a user to
draw an image while
simultaneously drawing two
or more copies of it.
• can also make smaller or
larger copies of an
• used is electric traction
railway applications for
taking power from
overhead HT wires. riginal
drawing.
30By Pooja Katkar

31. FBC-Inversion 3-(Double crank
mechanism) Coupling rod of a
locomotive/Locomotive Coupler
Locomotive Coupler
• AD =BC - cranks
• link CD acts as a coupling
rod and the link AB is fixed
• used for transmitting rotary
motion from one wheel to
the other wheel.
31By Pooja Katkar

32. 32By Pooja Katkar

33. 2. Single slider crank chain
Found in reciprocating steam engine
mechanism
• modification
of the basic
four bar chain
• mechanism
converts
rotary motion
into
reciprocating
motion and
vice versa.
33By Pooja Katkar

34. 2. Single slider crank chain
• consist of one sliding pair and three turning pairs.
• link 1 =frame of the engine, (fixed)
• link 2 = the crank
• link 3 =connecting rod
• link 4 =cross-head.
• As the crank rotates, the cross-head reciprocates in
the guides and thus the piston reciprocates in the
cylinder.
• How Slider Crank Mechanism Works.mp4
34By Pooja Katkar

35. SSC-Inversion 1 – Pendulum Pump/Bull
engine
• link 4 = fixed (i.e.cylinder
sliding pair)
• link 2 =the crank
• link 3 = connecting rod
oscillates about a pin pivoted
A
• Link 1 fixed with link 4 at A and
the piston attached to the
piston rod (link 1)
• Piston rod reciprocates
• The duplex pump which is
used to supply feed water to
boilers have two pistons
attached to link 1
35By Pooja Katkar

36. SSC-Inversion 1 – Pendulum Pump
• PENDULUM_PUMP_OR
_BULL_ENGINE_avi.mp
4
• handpump.webm
36By Pooja Katkar

37. SSC-Inversion 2- Rotary I.C.Engine
• consists of seven cylinders in
one plane
• all revolves about fixed centre
D,
• crank (link 2) is fixed
• connecting rod (link 4) rotates
• the piston (link 3) reciprocates
inside the cylinders forming
link 1.
• Gnome engine
37By Pooja Katkar

38. 38By Pooja Katkar

39. SSC-Inversion 3 – Oscillating Cylinder
Engine
• converts reciprocating motion
into rotary motion.
• the link 3 forming the turning
pair is fixed
• The link 3 = connecting rod of
a reciprocating steam engine
mechanism.
• crank (link 2) rotates
• piston attached to piston rod
(link 1) reciprocates
• cylinder (link 4) oscillates
about a pin pivoted to the
fixed link at A.
39By Pooja Katkar

40. 40By Pooja Katkar

41. SSC-Inversion 4 – Whithworth Quick
Return Mechanism
• used in shaping and slotting machines
• link CD (link 2) forming the turning pair is fixed
• link 2 corresponds to a crank in a reciprocating steam
engine
• driving crank CA (link 3) rotates at a uniform angular speed.
• The slider (link 4) attached to the crank pin at A slides along
the slotted bar PA (link 1) which oscillates at a pivoted point
D.
• The connecting rod PR carries the ram at R to which a
cutting tool is fixed.
• The motion of the tool is constrained along the line RD
produced, i.e. along a line passing through D and
perpendicular to CD.
41By Pooja Katkar

42. withworth quick return.webm
42By Pooja Katkar

43. SSC-Inversion 5 – Quick Return
Mechanism of Shaper
• shaping machines, slotting machines and in
rotary internal combustion engines
• AC (i.e. link 3) = turning pair is fixed
• Link 3 = connecting rod of a reciprocating
steam engine.
• CB = driving crank revolves with uniform
angular speed about the fixed centre C.
• A sliding block attached to the crank pin at B
slides along the slotted bar AP and thus
causes AP to oscillate about the pivoted point
A.
• A short link PR transmits the motion from AP
to the ram which carries the tool and
reciprocates along the line of stroke R1R2.
• The line of stroke of the ram (i.e. R1R2) is
perpendicular to AC produced.
• videos & imagesshaper machine.gif
• videos & imagesshaper4a.gif
43By Pooja Katkar

44. 3.Double Slider Chain
• consists of two turning pairs and two sliding
pairs
• link 2 and link 1 form one turning pair and link
2 and 3 form the second turning pair.
• The link 3 and 4 form one sliding pair and link
1 and link 4 form the second sliding pair.
44By Pooja Katkar

45. DSC Inversion 1 - Scotch Yoke
Mechanism
• either the link 1 or link 3 is
fixed
• fixed link 1 guides the frame.
• the link 2 (=crank) rotates
about B as centre,
• the link 4 (=frame)
reciprocates.
• APPLICATION : used for
converting rotary motion into
a reciprocating motion
videos & imagesScotch-Yoke.gif
45By Pooja Katkar

46. DSC Inversion 2 – Elliptical Trammel
• slotted plate (link 4)
• The fixed plate has two straight
grooves cut in it, at right angles to
each other.
• link 1 and link 3 = sliders and form
sliding pairs with link 4.
• link AB (link 2) is a bar which forms
turning pairs with links 1 and 3.
• When the links 1 and 3 slide along
their respective grooves, any point
on the link 2 such as P traces out an
ellipse on the surface of link 4, as
shown in Fig.
• A little consideration will show that
AP and BP are the semi-major axis
and semi-minor axis of the ellipse
respectively.
• Application :instrument used for
drawing ellipses.
videos & imageselliptical
trammel.gif
46By Pooja Katkar

47. DSC Inversion 3 – Oldham’s Coupling
videos & imagesOldham_coupler_animated_small.gif
videos & imagesoldham-coupling-animation.gif
videos & imagesOLDHAMS COUPLING.gif
47By Pooja Katkar

48. 48
•The shafts are coupled in such a way that if one shaft rotates, the other shaft
also rotates at the same speed.
•This inversion is obtained by fixing the link 2
•The shafts to be connected have two flanges (link 1 and link 3) rigidly
fastened at their ends by forging.
•The link 1 and link 3 form turning pairs with link 2.
•These flanges have diametrical slots cut in their inner faces
•The intermediate piece (link 4) which is a circular disc, have two tongues (i.e.
diametrical projections) T1 and T2 on each face at right angles to each other
•The tongues on the link 4 closely fit into the slots in the two flanges (link 1
and link 3).
• The link 4 can slide or reciprocate in the slots in the flanges.
•APPLICATION : used for connecting two parallel shafts whose axes are at a
small distance apart.
By Pooja Katkar

49. References
• Theory of Machines by Khurmi-Gupta
• Theory of Machines by S.S.Ratan
• Google images
49By Pooja Katkar