Group 1 INTRODUCTION TO KINEMATICS of BSME
- 1. At the end of the course, students will be able to, CO1:Describe the concepts ofmachines, mechanisms and related terminologies. CO2:Identify the mechanisms and predict their motions in mechanical components. CO3: Analyze planar mechanism for displacement, velocity and acceleration analytically and graphically. CO4:Analyze various motion transmission elements like gears, gear trains and cams. CO5: Utilize analytical, mathematical and graphical aspects of kinematics of machines effective design. for Course Outcomes
- 2. Kinematics of Machines CHAPTER 1: Introduction to Kinematics of Machines
- 3. Module 1 Introduction: Definitions Link or element, kinematic pairs, Degrees of freedom, Grubler's criterion (without derivation), Kinematic chain, Mechanism, Structure, Mobility of Mechanism, Inversion, Machine. Kinematic Chains and Inversions: Inversions of Four bar chain; Single slider crank chain and Double slider crank chain
- 4. Terminologies Machine (Input) load (output). •Device for transferringand/or transforming motion and force (power) from •A machine is a device which receives energy in some available form and utilizes source to the to do some work. or
- 5. Classification of Motion •Continuous rotation motion •Linear motion / Rectilinear Motion / •Intermittent motion •Angular Oscillations translatory motion
- 6. Basic Definitions Kinematic Chains and Inversions • Link or element • Kinematic pair • Kinematic chain • Mechanism, Machine & Structure • Degrees of freedom (DOF) • Grubler’s criterion •Double slider crank chain •Inversions of Four bar chain • Inversion •Single slider crank chain and
- 8. Kinematic Link or Element kinematic link (or simply link) or element. Each part of a machine, which moves relative to some other part, is known as a
- 9. e.g.: Fluid link: Rigid link : Types of Links • • belts, ropes, chains and wires A link formed by having a fluid in a receptacle and the motion is Link which does not undergo any deformation while transmitting motion. • Flexible link: Link which transmission of motion. transmittedthrough the fluidby pressure. e.g.: hydraulic presses, jacks and brakes. is partly deformed in a manner not to affect the
- 10. Classification of Links • • • • : Link with one Node (bucket of an excavator) Link connected to other links at two points Link connected to other links at three points Link connected to other links at four points Unary Link Binary link : Ternary link: Quaternary link:
- 11. Structure no relative motion An assembly of a no. of resistant bodies (members) having Examples: A railway bridge, a roof truss, machine frames. etc. between them and meant for carrying loads having straining action.
- 12. Difference Between a Machine and a Structure • • The parts of a machine move relative to one another, whereas the members of a structure do not move relative to one another • A machine transforms the available energy into some useful work, whereas in a structure no energy is transformed into useful work The links of a machine may transmit both power and motion, while the members of a structure transmit forces only (load bearing member).
- 13. Kinematic Pair Completely constrained Successfully constrained The two links or elements of a machine, when in contact with each other, are said to form a pair, If the relative motion between them is completely or successfully constrained (i.e. in a definite direction)
- 15. Example: Constrained Motions 1. Completely constrained motion The motion of a square bar in a square hole The motion of a shaft with collars at each end in a circular hole When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion.
- 16. 2. Incompletely constrained motion When the motion between a pair can take place in more than one direction, then it can be an incompletely constrained motion. E.g.: A circular bar or shaft in a circular hole It may either rotate or slide in a hole. These both motions have no relationship with the other (automobile wheel).
- 17. 3. Successfully constrained motion When the motion between the elements, forming a pair, Ex. Shaft in a foot-step bearing, I C engine valve, Piston inside an cylinder. is such that the constrained motion is not completed by itself, but by some other means
- 18. Classification of Kinematic Pairs According to the type of relative motion between the element 1. Sliding pair / Prismatic pair (P) reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed When the two elements of a pair are connected in such a way that one can only slide relative to the other, has a completely constrained motion. E.g.: The piston and cylinder, Cross-head and guides of a
- 19. 2. Turning Pair / Revolute Pair (R) Examples: Lathe spindle supported in headstock. When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link. Cycle wheels turning over their axles.
- 20. 3. Spherical pair (S) When the two elements of a pair are connected in such a way that one element turns or swivels about the other fixed element. Eg: The ball and socket joint. Attachment of a car mirror. Pen stand.
- 21. 4. Screw pair When the two elements of a pair are connected in such a way that one element can • • The lead screw of a lathe with nut Bolt with a nut turn about the other by screw threads. Examples:
- 22. 5. Cylindrical pair If the relative motion between the pairing elements is the combination of turning and sliding, then it is called as cylindrical pair.
- 23. 6. Rolling Pair E.g.: Ball and roller bearings, railway wheel rolling over a fixed rail When the two elements of a pair are connected in such a way that one rolls over another fixed link. Belt and pulley
- 24. element slides or rolls over the surface of the other. E.g. sliding pairs, turning pairs and screw pairs form lower pairs. According to the type / nature of contact between the elements / links. Classification of Kinematic Pairs surface contact, 1. Lower pair When the two elements of a pair have a and the surface of one
- 25. According to the type / nature of contact between the elements / links. 2. Higher pair Classification of Kinematic Pairs follower. E.g toothed gearing, belt and rope drives, ball and roller bearings and cam and .: between the two elements is partly turning and partly sliding. When the two elements of a pair have a and the motion line or point contact,
- 26. When the two elements of a pair are way that only required relative motion occurs. E.g.Lower pairs are self closed pair. When the two elements of a pair are mechanically but external forces, the pair is said to be a force-closed pair. E.g.: Cam and follower According to the Mechanical arrangement. in such a 1.Self closed pair 2. Force -closed pair Classification of Kinematic Pairs not connected are kept in contact by the action of connected together mechanically
- 27. Lower pair Force -closed pair Higher pair Self closed pair •Sliding pairs •Turning pairs •Screw pairs Rolling pair Kinematic Pairs
- 28. •Based on the possible motions (Few Important Types only) Name of Pair Letter Symbol D.O.F 2. Prismatic / Sliding Pair P 1 3. Helical / Screw Pair H 1 4. Cylindrical Pair C 2 5. Spherical / Globular Pair S (or) G 3 6. Flat / Planar Pair E 3 1. Revolute / Turning Pair R 1
- 30. 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. Assembly of links (Kinematic link / element) and Kinematic pairs to transmit required / specified output motion(s) for given input motion(s) Or
- 31. e.g. Mechanism • It may be used for transmitting or transforming motion printing machine, windshield wiper, robot arms • A mechanism maybe regarded as a machine in which each part is reduced to the simplest form to transmit the required motion. • When one of the links of a kinematic chain is fixed, the chain is known as mechanism
- 32. Degrees of Freedom (DOF) / Mobility of a Mechanism Number of independent coordinates, required to describe / specify the configuration or position of all the links of the mechanism, with respect to the fixed link at any given instant.
- 33. Degrees of freedom (DOF) In a kinematic pair, depending on the constraints imposed on the motion, the links may loose some of the six degrees of freedom.
- 34. J M n M>0 M=0 M<0 Grubler’s Criterion / Equation Grubler’s mobility equation 1 = No. of joints having 1 DOF M = 3 (n-1) -j - j If, 2 = No. of joints having 2 DOF = Mobility or Total no. of DOF = Total no. of links in a mechanism , It gives mechanism with M DOF , it gives a statically determinate structure , it gives statically indeterminate structure 1 2 J
- 35. Find the Degrees of Freedom
- 36. Find the Degrees of Freedom
- 37. Inversion of Mechanism kinematic chain. •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
- 38. 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).
- 39. Types of Kinematic Chains 1.Four bar chain or quadric cyclic chain 2. Single slider crank chain 3. Double slider crank chain
- 40. 1.Four bar chain or quadric chain • Four bar chain (mechanism) is the • Each of them forms a turning pair at A, B, C and D. The link that makes a complete revolution is called a crank. simplest and the • The four links may be of different lengths. • According to Grashof ’s law for a four bar mechanism, “the sum of the shortest and longest link lengths should not be greater than the sum of the remaining two link lengths” if there is to be continuous relative motion between the two links. basic kinematic chain and consists of four rigid links
- 41. 1.Four bar chain or quadric chain • • link CD (link 3) which connects the crank and lever is called The shortest link, will make a complete revolution relative to the other three links connecting rod or coupler. crank or driver. lever or rocker or follower • • The fixed link AB (link 1) is known as frame of the mechanism. The mechanism transforms rotary motion into oscillating motion. In Fig., AD (link 4 ) is a crank. link BC (link 2) which makes a partial rotation or oscillates is known as
- 43. • • In this mechanism, the links AD and BC (having equal length) act as cranks and are connected to the respective wheels. The link CD acts as a coupling rod. • The link AB is fixed in order to maintain a constant centre to centre distance between them. Purpose: Transmitting rotary motion from one wheel to the other wheel.
- 45. Purpose of this mechanism is to convert rotary motion into reciprocating motion. When the crank AB rotates about the fixed point A. The lever oscillates about another fixed point D. The end E of lever is connected to a piston rod which reciprocates in a cylinder.`
- 46. On displacement of the mechanism, the tracing point The four links are : fixed link at A, link AC, link CE and link BFD. Links CEand BFDact as levers. E at the end of thelink CE traces out approximately a straight line.
- 47. Single Slider Crank Chain & Inversion
- 48. 2. Single Slider Crank Chain
- 50. 1) reciprocates. When the crank (link 2) is given a rotary motion, the connecting rod (link 3) oscillates about a pin pivoted to the fixed link 4 at attached to the piston rod (link A. The piston Pendulum Pump or Bull Engine
- 51. Link 3 forming the turning pair is fixed and it corresponds to the connecting rod of a reciprocating steam engine mechanism. When the crank (link 2) rotates, the piston attached to piston rod (link 1) reciprocates and the cylinder (link 4) oscillates about a pin pivoted to the fixed link at A A
- 53. It consists of seven cylinders in one plane all revolve about fixed centre D. Cylinders form link 1, Crank (link 2) is fixed. When the connecting rod (link4) rotates, the piston (link 3) reciprocates inside the cylinder.
- 54. Radial Engine
- 55. the line of stroke R1R2 A mechanism used in shaping and slotting machines, where the metal is cut intermittently. • LinkAC(i.e.link3)isfixed. • Crank CB revolves with uniform angular speed about the fixed center C. • Sliding block attached to the crank pin at B slides along the slotted bar AP, thus causing AP to oscillate about the pivoted point A. • Short link PR transmits the motion from AP to the ram which carries the tool and reciprocates along
- 56. • in the clockwise direction. The forward or cutting stroke occurs when the • crank rotates from the position CB1 to CB2 (or through an angle β) in the clockwise direction. The return stroke occurs when the crank rotates from the position CB2 to CB1 (or through angle α)
- 58. Double Slider Crank Chain
- 59. • • • This inversion is obtained by fixing the slotted plate (link 4). fixed plate or link 4 has two straight grooves cut in it, at right angles to each other. link 1 and link 3, are known as sliders and form sliding pairs with link 4. • 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 • link AB (link 2) is a bar which forms turning pair with links 1 and 3.
- 60. Show that AP and BP are the semi-major axis and semi-minor axis of the ellipse. OXand OY as horizontal and vertical axes Now the co-ordinates of the point P on the link BA will be let the link BA is inclined at an angle θwith the horizontal, This is the equation of an ellipse
- 61. • Thismechanismisusedforconvertingrotarymotionintoareciprocatingmotion. • The inversion is obtained by fixing either the link 1 or link 3. link 1 is fixed. • In this mechanism, when the link 2 (crank) rotates about B as centre, (frame) reciprocates. 4 the link • Thefixed link 1guides the frame.
- 62. End of Module