TOM UNIT 1 PDF

1. Fundamentals and Types of Mechanism Course Outcomes: Apply knowledge and skill related to different mechanisms and its motion in given situation. Theory Learning Outcomes TLO 1.1: Identify various links and pairs in the given mechanism. TLO 1.2: Ide...

1. Fundamentals and Types of Mechanism Course Outcomes: Apply knowledge and skill related to different mechanisms and its motion in given situation. Theory Learning Outcomes TLO 1.1: Identify various links and pairs in the given mechanism. TLO 1.2: Identify various type motion in the given pair. TLO 1.3: Identify various kinematic chain in the given configuration. TLO 1.4: Estimate degree of freedom for given configuration. TLO 1.5: Explain different inversion of mechanism. TLO 1.6: Select suitable inversion of mechanism for different application. 1.1 Kinematics of Machines: - Definition of statics, Dynamics, Kinematics, Kinetics, Kinematic link and itstypes, Kinematic pair and its types, constrained motion and its types The Theory of Machines may be sub-divided into the following four branches: 1. Kinematics:- It is that branch of Theory of Machines which deals with the relative motion between the various parts of the machines. 2. Dynamic:-. 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 com- bined 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 ma- chine parts are at rest. The mass of the parts is assumed to be negligible. 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. A link or element need not to be a rigid body, but it must be a resistant body. A body is said to be a resistant body if it is capable of transmitting the required forces with negligible deformation. Thus a link should have the following two characteristics: It should have relative motion, and It must be a resistant body. A link may consist of several parts, which are rig- idly fastened together, so that they do not move relative to one another. For example, in a reciprocating steam engine, as shown in Fig. piston, piston rod and crosshead constitute one link; connecting rod with big and small end bearings constitute a second link; crank, crank shaft and flywheel a third link and the cylinder, engine frame and main bearings a fourth link. 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. However, as the deformation of a connecting rod, crank etc. of a reciprocating steam engine is not appreciable, they can be considered as rigid links. Fig A shows connecting rod and piston. They are rigid and separate link connected by pin joint. Fig B shows rigid link Gear 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 and transmit tensile forces only. Fig C shows flexible link belt and rigid link Pulley 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. Fig D Shows oil as fluid link which takes force from link 2 and transmit it to link 2 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. Classification of Kinematic Pairs The kinematic pairs may be classified according to the following considerations: 1. According to the type of relative motion between the elements. The kinematic pairs ac- cording to type of relative motion between the elements may be classified as discussed below: 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. 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, the crankshaft in a journal bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their axles etc. are the examples of a turning pair. A turning pair also has a completely constrained motion. 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 bearings are examples of rolling pair. 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 are examples of a screw pair. 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., are the examples of a spherical pair. 2. According to the type of contact between the elements. The kinematic pairs according to the type of contact between the elements may be classified as discussed below 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. 3. According to the type of closure. The kinematic pairs according to the type of closure between the elements may be classified as discussed below: 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. Fig shows unclosed pair which can be forced closed by using spring to achieve contact between cam and follower. Types of Constrained Motions 1. 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, as shown in Fig.  Square rod in square hole Shaft with collars in a circular hole The motion of a square bar in a square hole and the motion of a shaft with collars at each end in a circular hole are also examples of completely constrained motion. 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. Shaft in a circular hole. Shaft in a foot step bearing. 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 con- strained 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 (these are kept on their seat by a spring) and the piston reciprocating inside an engine cylinder are also the examples of successfully constrained motion. 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. In other words, a kinematic chain may be de- fined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained. If each link is assumed to form two pairs with two adjacent links, then the relation between the number of pairs ( P ) forming a kinematic chain and the number of links ( L ) may be expressed in the form of an equation L= 2 P - 4 --------------------(1) Since in a kinematic chain each link forms a part of two pairs, therefore there will be as many links as the number of pairs. Another relation between the number of links (L) and the number of joints ( J ) which constitute a kinematic chain is given by the expression : J =3/2 L - 2-------------------------(2) Joint (J) – It is connection of two links Types of joints Binary joint - If two links are join at a same connection it is called binary joint. fig shows chain with two binary joints named B. Ternary joints- If three links are join at a same connection it is known as ternary joint it is considered equivalent to 2 binary joints. fig shows chain with six ternary joints named T Quaternary joints- If Four links are join at a same connection it is known as quaternary joint it is considered equivalent to 3 binary joints. fig shows chain with one quaternary joints named Q. A) Consider the arrangement of three links A B, BC and CA with pin joints at A , B and C as shown in Fig. In this case, Number of links, L=3 Number of pairs, P=3 and number of joints, J=3 From equation (i), l = 2P – 4 or 3=2×3–4=2 i.e. L.H.S. > R.H.S. Now from equation (2), J = 3/2 L – 2  4 = 3/2 (4) – 2 4=2.5 L.H.S. > R.H.S. Since the arrangement of three links, as shown in Fig. does not satisfy the equations (i) and (ii) and the left hand side is greater than the right hand side, therefore it is not a kinematic chain and hence no relative motion is possible. Such type of chain is called locked chain and forms a rigid frame or structure which is used in bridges and trusses B) Consider the arrangement of four links A B, BC, CD and DA as shown in Fig. 5.7. In this case L= 4, P = 4, and J = 4 From equation (1), L=2P–4 4=2×4–4=4 i.e. L.H.S. = R.H.S. From equation J = 3/2 L – 2 (2), 4 = 3/2 (4) -2 L.H.S. = R.H.S.  Since the arrangement of four links, as shown in Fig. satisfy the equations (i) and (ii), therefore it is a kinematic chain of one degree of freedom. A chain in which a single link such as AD in Fig. is sufficient to define the position of all other links, it is then called a kinematic chain of one degree of freedom. A little consideration will show that in Fig. if a definite displacement is given to the link A D, keeping the link AB fixed, then the resulting displacements of the remaining two links BC and CD are also perfectly definite. Thus we see that in a four bar chain, the relative motion is completely constrained. Hence it may be called as a constrained kinematic chain, and it is the basis of all machines. C) Consider an arrangement of five links, as shown in Fig. In this case, L= 5, P = 5, and J= 5 From equation (i), L=2P–4 or 5=2×5–4 5< 6 i.e. L.H.S. < R.H.S. From equation (ii), J = 3/2 L – 2 5 = 3/2 (5) -2 L.H.S. < R.H.S. Since the arrangement of five links, as shown in Fig. 5.8 does not satisfy the equations and left hand side is less than right hand side, therefore it is not a kinematic chain. Such a type of chain is called unconstrained chain i.e. the relative motion is not completely constrained. This type of chain is of little practical importance D) Consider an arrangement of six links, as shown in Fig. This chain is formed by adding two more links in such a way that these two links form a pair with the existing links as well as form themselves a pair. In this case L = 6, P= 5, and J = 7 From equation (1), L= 2 P – 4 6=2×5–4=6 i.e. L.H.S. =R.H.S. From equation (2), J= 3 /2 (L) - 2 7= 3/2 (6) - 2 i.e. L.H.S. = R.H.S. Since the arrangement of six links, as shown in Fig. satisfies the equations (i.e. left hand side is equal to right hand side), therefore it is a kinematic chain. A chain having more than four links is known as compound kinematic chain. 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. In such cases, the various links or elements have to be designed to withstand the forces (both static and kinetic) safely. A little consideration will show that a mechanism may be regarded as a machine in which each part is reduced to the simplest form to transmit the required motion. Number of Degrees of Freedom for Plane Mechanisms In the design or analysis of a mechanism, one of the most important concern is the number of degrees of freedom (also called movability) of the mechanism. 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. It is possible to determine the number of degrees of freedom of a mechanism directly from the number of links and the number and types of joints which it includes. (a) Four bar chain. (b) Five bar chain. Consider a four bar chain, as shown in Fig. (a). A little consideration will show that only one variable such as Θ is needed to define the relative positions of all the links. In other words, we say that the number of degrees of freedom of a four bar chain is one. Now, let us consider a five bar chain, as shown in Fig. (b). In this case two variables such as Θ 1 and Θ 2 are needed to define completely the relative positions of all the links. Thus, we say that the number of degrees of freedom is two. In order to develop the relationship in general, consider two links AB and CD in a plane motion as shown in Fig. 5.14 (a). The link AB with co-ordinate system OXY is taken as the reference link (or fixed link). The position of point P on the moving link CD can be completely specified by the three variables, ie the co-ordinates of the point P denoted by x and y and the inclination Θ of the link CD with X-axis or link A B. In other words, we can say that each link of a mechanism has three degrees of freedom before it is connected to any other link. But when the link CD is connected to the link AB by a turning  pair at A , as shown in Fig. 5.14 (b), the position of link CD is now determined by a single variable Θ and thus has one degree of freedom. From above, we see that when a link is connected to a fixed link by a turning pair (i.e. lower pair), two degrees of freedom are destroyed. This may be clearly understood from Fig. 5.15, in which the resulting four bar mechanism has one degree of freedom (i.e. n = 1). Four bar mechanism Now let us consider a plane mechanism with l number of links. Since in a mechanism, one of the links is to be fixed, therefore the number of movable links will be (l – 1) and thus the total number of degrees of freedom will be 3 (l – 1) before they are connected to any other link. In general, a mechanism with l number of links connected by j number of binary joints or lower pairs (i.e. single degree of freedom pairs) and h number of higher pairs (i.e. two degree of freedom pairs), then the number of degrees of freedom of a mechanism is given by F = 3 (L – 1) – 2 J – h... (i) This equation is called Kutzbach criterion for the movability of a mechanism having Plane motion. If there are no two degree of freedom pairs (i.e. higher pairs), then h = 0. Substituting h = 0 in equation (i), we have F = 3 (L – 1) – 2Jj... (ii) Applic ation of Kutzba ch Criterion to Plane Mechanisms We have discussed in the previous article that Kutzbach criterion for determining the number of degrees of freedom or movability (n) of a plane mechanism is F = 3 (L – 1) – 2 J – h Fig a. fig b. Fig c. fig d fig e 1. The mechanism, as shown in Fig.(a), has three links and three binary joints, i.e. L = 3 and J = 3. h = 3 (3 – 1) – 2 × 3 = 0 2. The mechanism, as shown in Fig. (b), has four links and four binary joints, i.e.L = 4 and J= 4. h = 3 (4 – 1) – 2 × 4 = 1  3. The mechanism, as shown in Fig. 5 (c), has five links and five binary joints, i.e. L = 5, and J = 5. h = 3 (5 – 1) – 2 × 5 = 2 4. The mechanism, as shown in Fig. (d), has five links and six equivalent binary joints (because there are two binary joints at B and D, and two ternary joints at A and C), i.e. L = 5 and J = 6. h = 3 (5 – 1) – 2 × 6 = 0 5. The mechanism, as shown in Fig. (e), has six links and eight equivalent binary joints (because there are four ternary joints at A, B, C and D), i.e. L = 6 and J = 8. h = 3 (6 – 1) – 2 × 8 = – 1 It may be noted that (a) When n = 0, then the mechanism forms a structure and no relative motion between the links is possible, as shown in Fig. (a) and (d). (b) When n = 1, then the mechanism can be driven by a single input motion, as shown in Fig. (b). (c) When n = 2, then two separate input motions are necessary to produce constrained motion for the mechanism, as shown in Fig. (c). (d) When n = – 1 or less, then there are redundant constraints in the chain and it forms a statically indeterminate structure, as shown in Fig. (e). 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. A railway bridge, a roof truss, machine frames etc., are the examples of a structure. Difference Between a Machine and a Structure The following differences between a machine and a structure are important from the subject point of view: 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. The links of a machine may transmit both power and motion, while the members of a structure transmit forces only 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.  Inversion of Mechanism We have already discussed that when one of links is fixed in a kinematic chain, it is called a mechanism. So we can 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. Types of Kinematic Chains The most important kinematic chains are those which consist of four lower pairs, each pair being a sliding pair or a turning pair. The following three types of kinematic chains with four lower pairs are important from the subject point of view 1. Four bar chain or quadric cyclic chain, 2. Single slider crank chain, and 3. Double slider crank chain. 1. Inversions of Four Bar Chain 1. Beam engine (crank and lever mechanism). A part of the mechanism of a beam engine (also known as crank and lever mechanism) which consists of four links, is shown in Fig. In this mechanism, when the crank rotates about the fixed centre A , the lever oscillates about a fixed centre D. The end E of the lever CDE is connected to a piston rod which reciprocates due to the rotation of the crank. In other words, the purpose of this mechanism is to convert rotary motion into reciprocating motion  2. Coupling rod of a locomotive (Double crank mechanism). The mechanism of a coupling rod of a locomotive (also known as double crank mechanism) which consists of four links, is shown in Fig. In this mechanism, the links AD and BC (having equal length) act as cranks and are con- nected to the respective wheels. The link CD acts as a coupling rod and the link AB is fixed in order to maintain a constant centre to centre distance between them. This mechanism is meant for transmit- ting rotary motion from one wheel to the other wheel. 3. Watt’s indicator mechanism (Double lever mechanism). A *Watt’s indicator mechanism (also known as Watt's straight line mechanism or double lever mechanism) which consists of four links, is shown in Fig. The four links are : fixed link at A , link A C, link CE and link BFD. It may be noted that BF and FD form one link because these two parts have no relative motion between them. The links CE and BFD act as levers. The displacement of the link BFD is directly proportional to the pressure of gas or steam which acts on the indicator plunger. On any small displacement of the mechanism, the tracing point E at the end of the link CE traces out approximately a straight line  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. It is,usually, found in reciprocating steam engine mechanism. This type of mechanism converts rotary motion into reciprocating motion and vice versa. In a single slider crank chain, as shown in Fig. the links 1 and 2, links 2 and 3, and links 3 and 4 form three turning pairs while the links 4 and 1 form a sliding pair. The link 1 corresponds to the frame of the engine, which is fixed. The link 2 corresponds to the crank ; link 3 corresponds to the connecting rod and link 4 corresponds to cross-head. As the crank rotates, the cross-head reciprocates in the guides and thus the piston reciprocates in the cylinder. Inversions of Single Slider Crank Chain We have seen in the previous article that a single slider crank chain is a four-link mechanism. We know that by fixing, in turn, different links in a kinematic chain, an inversion is obtained and we can obtain as many mechanisms as the links in a kinematic chain. It is thus obvious, that four inversions of a single slider crank chain are possible. These inversions are found in the following mechanisms. 1. Pendulum pump or Bull engine. In this mechanism, the inversion is obtained by fixing the cylinder or link 4 (i.e. sliding pair), as shown in Fig. In this case, when the crank (link 2) rotates, the connecting rod (link 3) oscillates about a pin pivoted to the fixed link 4 at A and the piston attached to the piston rod (link 1) reciprocates. The duplex pump which is used to supply feed water to boilers have two pistons attached to link 1, as shown in Fig.  2. Oscillating cylinder engine. The arrangement of oscillating cylinder engine mechanism, as shown in Fig. is used to convert reciprocating motion into rotary motion. In this mechanism, the link 3 forming the turning pair is fixed. The link 3 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 3. Rotary internal combustion engine or Gnome engine. Sometimes back, rotary internal combustion engines were used in aviation. But now-a-days gas turbines are used in its place. It consists of seven cylinders in one plane and all revolves about fixed centre D, as shown in Fig. 5.25, while the crank (link 2) is fixed. In this mechanism, when the connecting rod (Link 4) rotates and piston (Link 3) reciprocates inside cylinder (link 1)  4. Crank and slotted lever quick return motion mechanism. This mechanism is mostly used in shaping machines, slotting machines and in rotary internal combustion engines. In this mechanism, the link AC (i.e. link 3) forming the turning pair is fixed, as shown in Fig. The link 3 corresponds to the connecting rod of a reciprocating steam engine. The driving crank CB 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. In the extreme positions, AP1 and AP2 are tangential to the circle and the cutting tool is at the end of the stroke. 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) in the clockwise direction. Since the crank has uniform angular speed, therefore,  5. Whitworth quick return motion mechanism. This mechanism is mostly used in shaping and slotting machines. In this mechanism, the link CD (link 2) forming the turning pair is fixed, as shown in Fig. The link 2 corresponds to a crank in a reciprocating steam engine. The 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 When the driving crank CA moves from the position C A1 to C A2 (or the link DP from the position DP1 to DP2) through an angle in the clockwise direction, the tool moves from the left hand end of its stroke to the right hand end through a distance 2 PD. Now when the driving crank moves from the position CA2 to CA1 (or the link DP from DP2 to DP1 ) through an angle in the clockwise direction, the tool moves back from right hand end of its stroke to the left hand end. A little consideration will show that the time taken during the left to right movement of the ram (i.e. during forward or cutting stroke) will be equal to the time taken by the driving crank to move from CA1 to CA2. Similarly, the time taken during the right to left movement of the ram (or during the idle or return stroke) will be equal to the time taken by the driving crank to move from C A2 to C A1. Since the crank link CA rotates at uniform angular velocity therefore time taken during the cutting stroke (or forward stroke) is more than the time taken during the return stroke. In other words, the mean speed of the ram during cutting stroke is less than the mean speed during the return stroke. The ratio between the time taken during the cutting and return strokes is given by Time of cutting stroke   360−  = = or Time of return stroke  360 −    6. Oscillating cylinder Engine In oscillating cylinder engine, the link 4 is made in the form of cylinder and a piston is fixed to end of link 1. The Piston reciprocates inside the cylinder provided to fixed link 3. The arrangement is known as oscillating cylinder engine in which Piston reciprocates in oscillating cylinder and crank rotates. 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. Inversions of Double Slider Crank Chain The following three inversions of a double slider crank chain are important from the subject point of view 1. Elliptical trammels. It is an instrument used for drawing ellipses. This inversion is obtained by fixing the slotted plate (link 4), as shown in Fig..The fixed plate or link 4 has two straight grooves cut in it, at right angles to each other. The link 1 and link 3, are known as sliders and form sliding pairs with link 4. The link AB (link 2) is a bar which forms turning pair 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. 5.34 (a). A little consideration will show that AP and BP are the semi-major axis and semi-minor axis of the ellipse respectively. This can be proved as follows  2. Scotch yoke mechanism. This mechanism is used for converting rotary motion into a reciprocating motion. The inversion is obtained by fixing either the link 1 or link 3. In Fig. 5.35, link 1 is fixed. In this mechanism, when the link 2 (which corresponds to crank) rotates about B as centre, the link 4 (which corresponds to a frame) reciprocates. The fixed link 1 guides the frame. 3. Oldham’s coupling. An oldham's coupling is used for connecting two parallel shafts whose axes are at a small distance apart. 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, as shown in Fig. 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, as shown in Fig. (b). 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, as shown in Fig. (c). 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 Question Bank 1. Define kinematic link and Kinematic Pair 2. State any two characteristics of link 3. State Rigid link with example 4. State flexible link with example 5. State fluid link with example 6. Classify Kinematic pairs 7. State kinematic Chain, Under constrained chain and locked chain 8. Define Structure, Kinematic chain, mechanism and machine. 9. Identify the type of chain for following configurations 10. State Kutzbatch Criteria 11. State difference Between a Machine and Structure 12. 13. 14. Identify number of links and pairs in following mechanism 15. Calculate Degree of freedom of following mechanisms. 16.