Basic Kinematics, Mechanisms and Inversions.pptx

A machine consists of a number of parts or bodies. Study of the mechanisms of the various parts or bodies from which the machine is assembled. This is
done by making one of the parts as fixed, and the relative
motion of other parts is determined with respect to the fixed part

1. Kinematics of Machinery Theory of Machines

2. Machines Energy Mechanical Work

3. Planar kinematic chain : all links move in parallel planes Spatial kinematic chain : link motion not restricted to a plane

4. 2/8/2024 Hareesha N G, Dept of Aero Engg, DSCE 5 LINKS FLEXIBLE RIGID FLUID 1.BINARY 2.TERNARY 3.QUATNARY Types Of Links

5. Link or element: It is the name given to any body which has motion relative to another. All materials have some elasticity. A rigid link is one, whose deformations are so small that they can be neglected in determining the motion parameters of the link. Binary link: Link which is connected to other links at two points. (Fig.a) Ternary link: Link which is connected to other links at three points. (Fig.b) Quaternary link: Link which is connected to other links at four points. (Fig. c) 2/8/2024 7

6. Types Of Constrained Motions 2/8/2024 8

7. Types of Constrained Motions Following are the three types of constrained motions : Completely constrained motion. 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. For example, the piston and cylinder (in a steam engine) form a pair and the motion of the piston is limited to a definite direction ( i.e. it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank. The motion of a square bar in a square hole, as shown in Fig., and the motion of a shaft with collars at each end in a circular hole, as shown in Fig., are also examples of completely constrained motion. 2/8/2024 9

8. 2. Incompletely constrained motion. When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion. The change in the direction of impressed force may alter the direction of relative motion between the pair. A circular bar or shaft in a circular hole, as shown in Fig ., is an example of an incompletely constrained motion as it may either rotate or slide in a hole. These both motions have no relationship with the other. 2/8/2024 10

9. 3. Successfully constrained motion When the motion between the elements, forming a pair, is such that the constrained motion is not completed by itself, but by some other means, then the motion is said to be successfully constrained motion. Consider a shaft in a foot-step bearing as shown in Fig. The shaft may rotate in a bearing or it may move upwards. This is a case of incompletely constrained motion. But if the load is placed on the shaft to prevent axial upward movement of the shaft, then the motion of the pair is said to be successfully constrained motion. The motion of an I.C. engine valve and the piston reciprocating inside an engine cylinder are also the examples of successfully constrained motion. 2/8/2024 11

10. 2/8/2024 Hareesha N G, Dept of Aero Engg, DSCE 13 TYPES OF PAIRS: 1 . SLIDING PAIR 2 . TURNING PAIR 3 . SPHERICAL PAIR 4. SCREW PAIR 5. ROLLING PAIR

11. 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, cross-head and guides of a reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed etc. are the examples of a sliding pair. A little consideration will show, that a sliding pair has a completely constrained motion. 2/8/2024 14 Classification of Kinematic Pairs

12. ( b) Turning pair or Revolutory 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. ( c) 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., are the examples of a spherical pair. 2/8/2024 15

13. ( d) 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 bearings are examples of rolling pair. ( e) 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 are examples of a screw pair. 2/8/2024 16

14. 2. According to the type of contact between the elements. 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. 2/8/2024 17

15. ( 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.

16. Degree of Freedom The number of independent parameters required to specify the position of all the links of the mechanism with respect to fixed link. Kutzbach Equation n = 3(l-1) – 2j – h n = No. of degree of freedom, l = No. of links, j= No. of lower pairs (No. of joints), If n = 1 then above equation can be written as 1 = 3(l-1)-2j 2j-3l+4 = 0 known as Gruebler’s equation A B C

17. Find the Degree of freedom

18. Four Bar Chain Mechanism If d ˃ a + b + c linkage cannot exist Crank, coupler and lever or rocker If a is to be crank then from (b) d + a ˂ b + c ---( i ) from ( c) d + c ˂ a + b ---(ii) and from (d) b ˂ c + (a-d) or d+b ˂ c + a ---(iii) Adding ( i ) and (ii) d ˂ b similarly adding (ii) and (iii) and (iii) & ( i ) d ˂ a and d ˂ c. Thus d is less than a, b and c

19. Grashoff’s law states that for a planar four–bar linkage, sum of the shortest and longest link-lengths must be less than or equal to the sum of the remaining two link lengths, if there to be a continuous relative rotation between two members s + l ≤ p + q

20. 2) Inversion of single slider crank chain In mechanism when there is one sliding member, the four bar chain is known as single slider crank chain. The inversion of slider crank chain are pendulum pump, oscillating cylinder engine, rotary internal combustion engine, crank and slotted lever quick-return motion mechanism and whitworth quick-return motion mechanism.

21. Whitworth quick-return motion Mechanism Second Inversion

22. Rotary internal combustion engine (Gnome): This mechanism is used in multi cylinder engine. It consists of several cylinders in one plane and all revolve about fixed center O, as shown figure. The crank (link 2) is fixed. When the connecting rod (link 3) rotates, the piston (link 4) reciprocates inside the cylinder forming link 1.

23. Rotary internal combustion engine diagram

24. Oscillating cylinder engine: In this mechanism link 3 is fixed . The link 2 rotates, the link 1 (piston rod) reciprocate and the link 4 (cylinder) oscillate about a pin B. Third Inversion

25. Crank and slotted lever quick-return motion mechanism: In this mechanism, link 1 is slider which slide in slotted lever. The slotted lever is link 4. link 3 is fixed where the center of crank attached. Link 2 is crank which rotates in clockwise direction. Link 4 is the arm which oscillates about point C. A short link DE transmits the motion with reciprocates with the tool along line of stroke.

26. The line of stroke is perpendicular to BC produced. This mechanism is mostly used in shaping machine and slotting machine.

27. Pendulum pump: When the sliding pair is fixed , the mechanism is known as pendulum pump. As the figure, link 2 to oscillates, link 3 (connecting rod) oscillates about a pin B and the piston attached to piston rod (link 1) reciprocates in the cylinder. Fourth Inversion

28. 3) Inversion of Double slider crank chain There are three type of inversion of double slider crank chain mechanism as: [a] Elliptical trammel [b] Scotch yoke mechanism [c] Oldham’s coupling

29. Elliptical Coupling: In this mechanism two slots are cut at right angles in a plane which is fixed. Two blocks slide in these two slots. Two sliding blocks form two links, which are of sliding type. Two sliding blocks are connected by one link. Point on this link at anywhere generate ellipse, when any ne blocks slides in its slot.

30. Elliptical Trammel

31. Scotch yoke mechanism: This mechanism converts rotary motion to reciprocating motion (simple harmonic motion). It is used in vibration exciter to produce vibration of desired frequency. This Chain has two revolute pairs and two prismatic pairs. The first inversion is with a link with revolute pair and prismatic pair is fixed.

32. Scotch yoke mechanism diagram

33. Oldham’s Coupling: When the distance between two shaft axes is small, motion is transmitted by oldham’s coupling. At the end of both the shafts there is flanges. This flange forms links 2 and 4. Both this links forms a turning pair with link 3. There is a diametrical slot on both the flange. An intermediate piece have a diametrical outside tongues at right angle on both sides. When the driving shaft is rotates, the intermediate piece rotates as well as sides in groove. This intermediate piece also rotates the driven shaft by sliding as well as rotating motion.