KINEMATICS OF MACHINERY Presented by VVR MURTHY M

KINEMATICS OF MACHINERY Presented by VVR MURTHY M. Tech, Assistant Professor DEPARTMENT OF MECHANICAL ENGINEERING VISAKHA INSTITUTE OF ENGINEERING & TECHNOLOGY

Mechanics Dynamics Kinetics 11/10/2016 Statics Kinematics By - T. S. SENTHILKUMAR/AP 2

• The branch of scientific analysis that deals with motions, time and forces is called mechanics. • It is divided in to two parts statics and dynamics. 11/10/2016 By - T. S. SENTHILKUMAR/AP 3

STATICS • It deals with the analysis of stationary systems. But time is not considered. DYNAMICS • It deals with the systems that change with time. 11/10/2016 By - T. S. SENTHILKUMAR/AP 4

KINEMATICS • It is the study of motion, quite apart from the forces which produce that motion. • It is the study of position, displacement, rotation, speed, velocity and acceleration. KINETICS • It is the study of motion and its causes 11/10/2016 By - T. S. SENTHILKUMAR/AP 5

� The subject matter which deals with this geometric constant of relative motion, without any reference to the cause of the motion that is the force is called kinematics. � For the study of kinematics, a machine may be referred to as a mechanism, which is a combination of inter connected rigid bodies capable of relative motion. 11/10/2016 By - T. S. SENTHILKUMAR/AP 6

� Machinery is defined as a mechanical device or the parts that keep something working. � Machines or machine parts considered as a group. � The working parts of a particular machine. � An assemblage of machines. � The parts of a machine collectively. � An assemblage of machines or mechanical apparatuses 11/10/2016 By - T. S. SENTHILKUMAR/AP 7

• It is defined as the combination of rigid or resistance bodies assembled in such a way that the motion of one causes constrained and predictable motion to others is known as mechanism. • If one of the links of a kinematic chain is fixed, then the chain is known as mechanism. 11/10/2016 By - T. S. SENTHILKUMAR/AP 8

�An assembly of moving parts performing a complete functional motion. � A mechanism is a device designed to transform input forces and movement into a desired set of output forces and movement. � Mechanisms generally consist of moving components such as gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches, and structural components such as the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine elements such as splines, pins and keys. 11/10/2016 By - T. S. SENTHILKUMAR/AP 9

• It is defined as a device which receives energy and transforms it into some useful work. • If the mechanism is used to transmit power (or) to do work, then it is known as machine. • The main function of the machine is to obtain mechanical advantage. 11/10/2016 By - T. S. SENTHILKUMAR/AP 10

� We can define machine as a device for transferring and transforming motion and force or power from the input that is, the source to the output that is the load. � The motion needs to be transformed as it is being transferred from the source to the load. 11/10/2016 By - T. S. SENTHILKUMAR/AP 11

11/10/2016 By - T. S. SENTHILKUMAR/AP 12

• It is a resistant body or assembly of resistant body of a machine connecting other parts of the machine with relative motion between them. • There are three types of links available in order to transmit motion. They are as follows: » Rigid link » Flexible link » Fluid link 11/10/2016 By - T. S. SENTHILKUMAR/AP 13

Rigid link A rigid link is one which does not undergo any deformation while transmitting motion. Practically rigid link does not exists. Ex : crank shaft, piston etc. , Flexible link A flexible link is one which undergoes partial deformation without affecting the transfer motion. Ex : ropes, belts, chains, springs etc. , Fluid link A fluid link is a link which has fluid inside the container and motion is transmitted through the fluid by pressure or compression. Ex: fluids used in hydraulic press, hydraulic jack, hydraulic crane etc. , 11/10/2016 By - T. S. SENTHILKUMAR/AP 14

Binary link, Ternary link, Quaternary link 11/10/2016 By - T. S. SENTHILKUMAR/AP 15

• A joint of two links that permits relative motion is called pair. Types of kinematic pair 1. Nature of relative motion between the links. 2. Nature of contact between the links. 3. Nature of mechanical arrangement. 11/10/2016 By - T. S. SENTHILKUMAR/AP 16

Nature of relative motion » Sliding pair » Turning pair » Cylindrical pair » Rolling pair » Spherical pair » Helical pair Nature of contact » Lower pair » Higher pair Nature of mechanical constraint 11/10/2016 » Closed pair » Unclosed p. Bayi-r. T. S. SENTHILKUMAR/AP 17

Sliding pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 18

Turning pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 19

Cylindrical pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 20

Rolling pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 21

Spherical pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 22

Helical pair or screw pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 23

Lower pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 24

Higher pair 11/10/2016 By - T. S. SENTHILKUMAR/AP 25

Closed pair • When two elements of a pair are held together mechanically, they constitute a closed pair. Ex : All pair Un closed pair • When two elements of a pair are not held together mechanically, they constitute a unclosed pair. Ex : cam and follower 11/10/2016 By - T. S. SENTHILKUMAR/AP 26

• If the last link is joined to first link to transmit definite motion, then it is known as kinematic chain. • To determine the given assemblage of links form the kinematic chain or not: • 11/10/2016 The equations are: = 2 p – 4 j = (3/2) * l – 2 Where, l = number p = number j = number Byof- T. S. SENTHILKUMAR/AP joints two l of of links pairs 27

Completely Constrained Motions Uncompletely Constrained Motion Successfully Constrained Motion 11/10/2016 By - T. S. SENTHILKUMAR/AP 28

JOINTS Binary joint 11/10/2016 Ternary joint By - T. S. SENTHILKUMAR/AP Quaternary joint 29

� The analysis of mechanism is the number of degrees of freedom, also called the mobility of the device. � The mobility of a mechanism is defined as the number of input parameters which must be controlled independently in order to bring the device in to a particular position. � It is the number of independent coordinates required to describe the position of a body in space. 11/10/2016 By - T. S. SENTHILKUMAR/AP 30

11/10/2016 By - T. S. SENTHILKUMAR/AP 31

� Movability includes the six degrees of freedom of the device as a whole, as through the ground link were not fixed and thus applies to a kinematic chain. � Mobility neglects these and considers only the internal motions, thus applying to a mechanism. 11/10/2016 By - T. S. SENTHILKUMAR/AP 32

� A link is to have ‘n’ degree of freedom if it has n independent variables associated with its position in the plane. 11/10/2016 By - T. S. SENTHILKUMAR/AP 33

� Then the number of degree of freedom of a mechanism (n) is given by, n = 3 (l-1) – 2 j – h where, l = number of links j = number of binary joints h = number of higher pairs � This equation is called kutzbach criterion for the mobility of a mechanism. � If there is no higher pair, then h = 0. then kutzbach criterion, n = 3 (l-1) – 2 j 11/10/2016 By - T. S. SENTHILKUMAR/AP 34

• Mechanism with lower pairs – Three bar mechanism – Four bar mechanism – Five bar mechanism – Six bar mechanism • Mechanism with higher pairs 11/10/2016 By - T. S. SENTHILKUMAR/AP 35

n = 6(l-1) – 5 P 1 – 4 P 2 – 3 P 3 – 2 P 4 – 1 P 5 Where, n = Number of degree of freedom l = Number of links P 1 = Number of pair having one degree of freedom P 2 = Number of pair having two degree of freedom 11/10/2016 By - T. S. SENTHILKUMAR/AP 36

• Grubler’s mechanism is obtained by substituting n = 1 and h = 0 in Kutzbach criterion as below. we know that, n = 3 (l-1) – 2 j - h l = 3 (l -1) – 2 j or 3 l – 2 j – 4 = 0 This equation is known as Grubler’s criterion for plane mechanism 11/10/2016 By - T. S. SENTHILKUMAR/AP 37

We know that Kutzbach criterion for spatial mechanism is n = 6(l-1) – 5 P 1 – 4 P 2 – 3 P 3 – 2 P 4 – 1 P 5 substitute n = 1; P 2, P 3 , … P 5 = 0 1 = 6(l-1) – 5 P 1 (or) 6 l – 5 P 1 – 7 = 0 This equation is known as Grubler’s equation for spatial mechanism. 11/10/2016 By - T. S. SENTHILKUMAR/AP 38

• When one of the links of kinematic chain is fixed, then the chain is known as mechanism. 11/10/2016 By - T. S. SENTHILKUMAR/AP 39

1. Simple mechanism 2. Compound mechanism 11/10/2016 By - T. S. SENTHILKUMAR/AP 40

Kinematic Pair When Connected As Per Kutzbach’s Criterion Kinematic Chain When Forces And Couples Are Transmitted Mechanism When One Link Is Fixed Machine 11/10/2016 By - T. S. SENTHILKUMAR/AP 41

The method of obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of the mechanism. 11/10/2016 By - T. S. SENTHILKUMAR/AP 42

Kinematic chain Four bar chain 11/10/2016 Slider crank chain By - T. S. SENTHILKUMAR/AP Double crank chain 43

11/10/2016 By - T. S. SENTHILKUMAR/AP 44

Inversion Of Four Bar Chain Beam Engine 11/10/2016 Coupled Locomotiv e Wheels Watt’s Indicator Mechanis m By - T. S. SENTHILKUMAR/AP Pantograph Ackerman n Mechanis m 45

First inversion Beam Engine second Inversion Coupling rod of locomotive Watt’s Indicator Mechanism Third Inversion 11/10/2016 Pantograph Ackermann Steering By - T. S. SENTHILKUMAR/AP 46

Beam engine • Mechanism. Gifinversion of four bar chainbeamengine-o. Gif 11/10/2016 By - T. S. SENTHILKUMAR/AP 47

Coupling rod of a locomotive 11/10/2016 By - T. S. SENTHILKUMAR/AP 48

Watt’s indicator mechanism 11/10/2016 By - T. S. SENTHILKUMAR/AP 49

Pantograph 11/10/2016 By - T. S. SENTHILKUMAR/AP 50

ACKERMANN STEERING 11/10/2016 By - T. S. SENTHILKUMAR/AP 51

11/10/2016 By - T. S. SENTHILKUMAR/AP 52

Single slider crank chain Reciprocating engine Reciprocating compressor Whitworth quick return mechanism Rotary or Gnome engine Crank and slotted lever mechanism Oscillating cylinder engine Bull engine 11/10/2016 Pump engine By - T. S. SENTHILKUMAR/AP 53

First Inversion Second Inversion Third Inversion Fourth Inversion 11/10/2016 Reciprocating engine Reciprocating compressor Whitworth quick return mechanism Rotary engine Oscillating cylinder engine Crank and slotted lever mechanism Bull Engine Hand Pump By - T. S. SENTHILKUMAR/AP 54

• Reciprocating engine 11/10/2016 By - T. S. SENTHILKUMAR/AP 55

• Reciprocating compressor 11/10/2016 By - T. S. SENTHILKUMAR/AP 56

• Whitworth Quick Return Mechanism 11/10/2016 By - T. S. SENTHILKUMAR/AP 57

• Rotary Engine 11/10/2016 By - T. S. SENTHILKUMAR/AP 58

• Oscillating Cylinder Engine 11/10/2016 By - T. S. SENTHILKUMAR/AP 59

• Crank and Slotted lever Quick return Mechanism basic 1_quickreturn. gif 11/10/2016 By - T. S. SENTHILKUMAR/AP 60

• Pendulum pump or bull engine 11/10/2016 By - T. S. SENTHILKUMAR/AP 61

• Hand pump 11/10/2016 By - T. S. SENTHILKUMAR/AP 62

11/10/2016 By - T. S. SENTHILKUMAR/AP 63

Double Slider Crank Chain Elliptical Trammel 11/10/2016 Scotch Yoke Mechanism By - T. S. SENTHILKUMAR/AP Oldham Coupling 64

Elliptical Trammel 11/10/2016 By - T. S. SENTHILKUMAR/AP 65

Scotch Yoke Mechanism 11/10/2016 By - T. S. SENTHILKUMAR/AP 66

Oldham's Coupling 11/10/2016 By - T. S. SENTHILKUMAR/AP 67

• Oldham's Coupling 11/10/2016 By - T. S. SENTHILKUMAR/AP 68

11/10/2016 By - T. S. SENTHILKUMAR/AP 69

11/10/2016 By - T. S. SENTHILKUMAR/AP 70

• Stationary screws with travelling nuts • Stationary nuts with travelling screws • Single and double acting hydraulic and pneumatic cylinders. 11/10/2016 By - T. S. SENTHILKUMAR/AP 71

11/10/2016 By - T. S. SENTHILKUMAR/AP 72

• C-Clamp 11/10/2016 By - T. S. SENTHILKUMAR/AP 73

• This type of mechanism produces a swinging or rocking motion of a link. The motion is generally less than 360 o and is an oscillatory motion. Toothed Rack System • This is simply a rotating arm (b) with a link fitted with a toothed rack (c) which meshes with a gear (d) to produce a rocking motion of the gear. 11/10/2016 By - T. S. SENTHILKUMAR/AP 74

Crank and Rocker Mechanism • This is simply a four bar linkage (the frame provides the first link). The operating characteristics are dependent on the length of the links and the design of the frame setting the pivot points. . Rotation of the arm (b) produces a rocking motion of arm (d). 11/10/2016 By - T. S. SENTHILKUMAR/AP 75

Crank and Rocker Mechanism 11/10/2016 By - T. S. SENTHILKUMAR/AP 76

Quick Return linkage • The arm (b) rotates and results in a rocking motion of arm (d)via the slider (c). The action is a quick return action because the angle (b) rotates through in one direction , assumed to be the forward direction, is greater than the angle which result in the return motion. 11/10/2016 By - T. S. SENTHILKUMAR/AP 77

Quick Return linkage 11/10/2016 By - T. S. SENTHILKUMAR/AP 78

Cam and Follower Mechanism • Rotation of the cam (c) produces a rocking motion of the lever (d) via the sliding interface (b). The arrangement only identifies the principle involved. In practice some means would have to be provided to ensure the lever is maintained in contact with the lever. 11/10/2016 By - T. S. SENTHILKUMAR/AP 79

Cam and Follower Mechanism 11/10/2016 By - T. S. SENTHILKUMAR/AP 80

• This mechanism is for rectilinear motion 11/10/2016 By - T. S. SENTHILKUMAR/AP 81

• This mechanism is used to regulate the movement of clock. 11/10/2016 By - T. S. SENTHILKUMAR/AP 82

11/10/2016 By - T. S. SENTHILKUMAR/AP 83

11/10/2016 By - T. S. SENTHILKUMAR/AP 84

• When a mechanism is desired which is capable of delivering output rotation in the either direction, some form of reversing mechanism is required. • Ex : gear shifting 11/10/2016 By - T. S. SENTHILKUMAR/AP 85

11/10/2016 By - T. S. SENTHILKUMAR/AP 86

11/10/2016 By - T. S. SENTHILKUMAR/AP 87

11/10/2016 By - T. S. SENTHILKUMAR/AP 88

• C: UserssenthilDesktopGeneva_mechanism _6 spoke_animation. gif 11/10/2016 By - T. S. SENTHILKUMAR/AP 89

Application of the Geneva drive • One is movie projectors : the film does not run continuously through the projector. Instead, the film is advanced frame by frame, each frame standing still in front of the lens for 1/24 of a second 11/10/2016 By - T. S. SENTHILKUMAR/AP 90

11/10/2016 By - T. S. SENTHILKUMAR/AP 91

• Peaucellier Mechanism C: UserssenthilDesktopPeaucellier_linkage_anim ation. gif 11/10/2016 By - T. S. SENTHILKUMAR/AP 92

• Robert’s Mechanism C: UserssenthilDesktopRoberts_linkage. gif 11/10/2016 By - T. S. SENTHILKUMAR/AP 93

• Chebychev Mechanism C: UserssenthilDesktopChebyshev_linkage. gif 11/10/2016 By - T. S. SENTHILKUMAR/AP 94

• This connectors are used when one slider is to drive another slider. 11/10/2016 By - T. S. SENTHILKUMAR/AP 95

• In an automobile engine a valve must open, remain open for a period of time, and then close. Ex : cam and follower 11/10/2016 By - T. S. SENTHILKUMAR/AP 96

• The connecting rod of a planar four bar linkage may be imagined as an infinite plane extending in all directions but pin connected to the input and output links. • Then, during motion of the linkage, any point attached to the plane of the coupler generates some path with respect to the fixed link, this path is called coupler curve. 11/10/2016 By - T. S. SENTHILKUMAR/AP 97