Fundamentals of Kinematics and Mechanisms
2 likes3,982 views
The document discusses the fundamentals of machine theory, focusing on kinematics and mechanisms, including types of links, kinematic pairs, and various chains and mechanisms like four bar and slider crank chains. It distinguishes machines from structures, defines various types of constrained motions, and introduces concepts like degree of freedom and inversion of mechanisms. Additionally, the document covers steering gear mechanisms and the criteria for assessing the mobility of mechanisms.
Fundamentals of Kinematics and Mechanisms
- 1. THEORY OF MACHINE FUNDAMENTALS OF KINEMATICS AND MECHANISMS By Mr. Keshav R. Pagar Assistant Professor Mechanical Engineering Department keshavpagar04@gmail.com
- 2. CONTENT Kinematic link, Types of links, Kinematic pair, Types of constrained motions, Types of Kinematic pairs, Kinematic chain, Types of joints, Mechanism, Machine, Degree of freedom (Mobility),Kutzbach crieterion, Grubler’s criterion. Four bar chain and its inversions, Grashoff’s law, Slider crank chain and its inversions, Double slider crank chain and its inversions. Straight line mechanisms such as: Peaucellier Mechanism, Scott Russell Mechanism, Grasshopper Mechanism, watt mechanism. Equivalent linkage of mechanisms., Steering gear mechanisms: Condition for correct steering, Davis steering gear mechanism, Ackermann steering gear mechanism.
- 3. INTRODUCTION Theory of Machines may be defined as that branch of Engineering-science, which deals with the study of relative motion between the various parts of a machine, and forces which act on them. 1. Kinematics. It is that branch of Theory of Machines which deals with the relative motion between the various parts of the machines. 2. Dynamics. It is that branch of Theory of Machines which deals with the forces and their effects, while acting upon the machine parts in motion. 3. Kinetics. It is that branch of Theory of Machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts. 4. Statics. It is that branch of Theory of Machines which deals with the forces and their effects while the machine parts are at rest. The mass of the parts is assumed to be negligible.
- 4. KINEMATIC LINK OR ELEMENT Each part of a machine, which moves relative to some other part, is known as a kinematic link (or simply link) or element. Link should have the following two characteristics: It should have relative motion, and It must be a resistant body.
- 5. TYPES OF LINKS 1. Rigid link. A rigid link is one which does not undergo any deformation while transmitting motion. Strictly speaking, rigid links do not exist. 2. Flexible link. A flexible link is one which is partly deformed in a manner not to affect the transmission of motion. For example, belts, ropes, chains and wires are flexible links 3. Fluid link. A fluid link is one which is formed by having a fluid in a receptacle and the motion is transmitted through the fluid by pressure or compression only, as in the case of hydraulic presses, jacks and brakes.
- 6. STRUCTURE It is an assemblage of a number of resistant bodies (known as members) having no relative motion between them and meant for carrying loads having straining action. Ex. A railway bridge, a roof truss, machine frames etc., are the examples of a structure.
- 7. DIFFERENCE BETWEEN A MACHINE AND A STRUCTURE The following differences between a machine and a structure are: 1. The parts of a machine move relative to one another, whereas the members of a structure do not move relative to one another. 2. A machine transforms the available energy into some useful work, whereas in a structure no energy is transformed into useful work. 3. The links of a machine may transmit both power and motion, while the members of a structure transmit forces only.
- 8. TYPES OF LINK BASED ON CONNECTIONS OR ATTACHMENTS
- 9. IDENTIFY NO OF LINKS Binary Link Ternary Link Quaternary Link
- 10. TYPES OF CONSTRAINED MOTIONS Completely constrained motion Incompletely constrained motion Successfully constrained motion
- 14. KINEMATIC PAIR 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), the pair is known as kinematic pair.
- 15. CLASSIFICATION OF KINEMATIC PAIRS 1. According to the type of relative motion between the elements A. Sliding pair. When the two elements of a pair are connected in such a way that one can only slide relative to the other, the pair is known as a sliding pair. The piston and cylinder, sliding pair has a completely constrained motion. B. Turning pair. 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, the pair is known as turning pair. A shaft with collars at both ends fitted into a circular hole, A turning pair also has a completely constrained motion.
- 16. C. Rolling pair. When the two elements of a pair are connected in such a way that one rolls over another fixed link, the pair is known as rolling pair. Ball and roller D. Screw pair. When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut, and bolt with a nut E. Spherical pair. When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair. The ball and socket joint, attachment of a car mirror, pen stand etc.,
- 18. 2. According to the type of contact between the elements. (a) Lower pair. When the two elements of a pair have a surface contact when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs. (b) Higher pair. When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding then the pair is known as higher pair. A pair of friction discs, toothed gearing, belt and rope drives, ball and roller bearings and cam and follower are the examples of higher pairs.
- 19. 3. According to the type of closure. (a) Self closed pair. When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair. (b) Force - closed pair. When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.
- 20. TYPES OF JOINTS IN A CHAIN 1. Binary joint. When two links are joined at the same connection, the joint is known as binary joint. 2. Ternary joint. When three links are joined at the same connection, the joint is known as ternary joint. It is equivalent to two binary joints as one of the three links joined carry the pin for the other two links. 3. Quaternary joint. When four links are joined at the same connection, the joint is called a quaternary joint. It is equivalent to three binary joints.
- 21. TYPES OF JOINTS 1. Binary Joint 2. Ternary Joint 3. Quaternary Joint
- 22. 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. number of pairs ( p ) forming a kinematic chain and the number of links ( l ), number of joints ( j ). This equations are applicable only to kinematic chains
- 24. MECHANISM When one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion e.g. engine indicators, typewriter etc. A mechanism with four links is known as simple mechanism, and the mechanism with more than four links is known as compound mechanism. When a mechanism is required to transmit power or to do some particular type of work, it then becomes a machine.
- 25. NUMBER OF DEGREES OF FREEDOM It is defined as the number of input parameters (usually pair variables) which must be independently controlled in order to bring the mechanism into a useful engineering purpose. (h) number of higher pairs, number of links ( l ), number of joints ( j ). This equation is called Kutzbach criterion for the movability of a mechanism having plane motion.
- 26. GRUBLER’S CRITERION FOR PLANE MECHANISMS The Grubler’s criterion applies to mechanisms with only single degree of freedom joints where the overall movability of the mechanism is unity. Substituting n = 1 and h = 0 in Kutzbach equation. This equation is known as the Grubler's criterion for plane mechanisms with constrained motion.
- 27. INVERSION OF MECHANISM when one of links is fixed in a kinematic chain, it is called a mechanism. So to obtain as many mechanisms as the number of links in a kinematic chain by fixing, in turn, different links in a kinematic chain. This method of obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of the mechanism
- 28. TYPES OF KINEMATIC CHAINS 1. Four bar chain or quadric cyclic chain, 2. Single slider crank chain, and 3. Double slider crank chain
- 30. FOUR BAR CHAIN kinematic chain is a combination of four or more kinematic pairs, such that the relative motion between the links or elements is completely constrained. 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
- 31. The shortest link, will make a complete revolution relative to the other three links, Such a link is known as crank or driver. AD (link 4 ) is a crank. The link BC (link 2) which makes a partial rotation or oscillates is known as lever or rocker or follower The link CD (link 3) which connects the crank and lever is called connecting rod or coupler. The fixed link AB (link 1) is known as frame of the mechanism.
- 32. 1. INVERSIONS OF FOUR BAR CHAIN 1. Beam engine (crank and lever mechanism)
- 33. 2. Coupling rod of a locomotive (Double crank mechanism).
- 34. 3. Watt’s indicator mechanism (Double lever mechanism).
- 35. 2. SINGLE SLIDER CRANK CHAIN A single slider crank chain is a modification of the basic four bar chain. It consist of one sliding pair and three turning pairs
- 36. INVERSIONS OF SINGLE SLIDER CRANK CHAIN 1. Pendulum pump or Bull engine
- 37. 2. Oscillating cylinder engine
- 38. 3. ROTARY INTERNAL COMBUSTION ENGINE OR GNOME ENGINE
- 39. 4. CRANK AND SLOTTED LEVER QUICK RETURN MOTION MECHANISM
- 40. 5. WHITWORTH QUICK RETURN MOTION MECHANISM
- 41. 3. DOUBLE SLIDER CRANK CHAIN A kinematic chain which consists of two turning pairs and two sliding pairs is known as double slider crank chain
- 42. INVERSIONS OF DOUBLE SLIDER CRANK CHAIN 1. Elliptical trammels
- 43. 2. SCOTCH YOKE MECHANISM
- 45. STRAIGHT LINE MECHANISMS 1. Peaucellier mechanism
- 46. 2. SCOTT RUSSELL’S MECHANISM
- 49. STEERING GEAR MECHANISM The steering gear mechanism is used for changing the direction of two or more of the wheel axles with reference to the chassis, so as to move the automobile in any desired path.
- 50. Let a = Wheel track, b = Wheel base, and c = Distance between the pivots A and B of the front axle. This is the fundamental equation for correct steering
- 52. ACKERMAN STEERING GEAR The Ackerman steering gear mechanism is much simpler than Davis gear. The difference between the Ackerman and Davis steering gears are : 1. The whole mechanism of the Ackerman steering gear is on back of the front wheels; whereas in Davis steering gear, it is in front of the wheels. 2. The Ackerman steering gear consists of turning pairs, whereas Davis steering gear consists of sliding members.
- 54. END