Met 305 tutorial-0_simple_mechanisms
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Met 305 tutorial-0_simple_mechanisms Document Transcript

  • 1. MET 305 MECHANICS OF MACHINES THEORY-1 MECHANISMS Definitions and Terminology1. IntroductionThe subject Theory of Machines may be defined as that branch of Engineering-science, which dealswith the study of relative motion between the various parts of a machine, and forces which act onthem. The knowledge of this subject is very essential for an engineer in designing the various parts ofa machine.1.1 Sub-divisions of Theory of MachinesThe 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. 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.1.2 A machine is a device which receives energy and transforms it into some useful work. Amachine consists of a number of parts or bodies. In this chapter, we shall study themechanisms of the various parts or bodies from which the machine is assembled. This isdone by making one of the parts as fixed, and the relative motion of other parts isdetermined with respect to the fixed part.2. Kinematic link or Element Any part of a machine, which moves relative to some other part, is known as a kinematiclink (or simply link) or an element. A link may consist of several parts, which are rig idlyfastened together, so that they do not move relative to one another. For example, in areciprocating steam engine, as shown above, crank, connecting rod, piston, engine frameand main bearings are the four links.A link or an element need not to be a rigid body, but it must be a resistant body. A body issaid to be a resistant body if it is capable of transmitting the required forces with negligibledeformation. Thus a link should have the following two characteristics:YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 2. MET 305 MECHANICS OF MACHINES THEORY-1 1. It should have relative motion, and 2. It must be a resistant body.2.1 Types of LinksIn order to transmit motion, the driver and the follower may be connected by the followingthree types of links:2.1.1. Rigid link A rigid link is one, which does not undergo any deformation whiletransmitting motion. Strictly speaking, rigid links do not exist. However, as the deformationof a connecting rod, crank etc. of a reciprocating steam engine is not appreciable, they canbe considered as rigid links.2.1.2. Flexible link A flexible link is one which is partly deformed in a manner not to affectthe transmission of motion. For example, belts, ropes, chains and wires are flexible links andtransmit tensile forces only.2.1.3. Fluid link. A fluid link is one which is formed by having a fluid in a receptacle and themotion is transmitted through the fluid by pressure or compression only, as in the case ofhydraulic presses, jacks and brakes.2.2 StructureIt is an assemblage of a number of resistant bodies (known as members) having no relativemotion between them and meant for carrying loads having straining action. A railwaybridge, a roof truss, machine frames etc., are the examples of a structure.2.3 Difference between a Machine and a Structure (frame)The following are the main differences between a machine and a structure. 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.3. Kinematic pairWhen two links or elements are connected in such a way that the relative motion betweenthem is completely or successfully constrained, they form a kinematic pair.3.1 Types of Constrained MotionsFollowing are the three types of constrained motions:-3.1.1 Completely constrained motionYANBU INDUSTRIAL COLLEGE 1/11/2013
  • 3. MET 305 MECHANICS OF MACHINES THEORY-1When the motion between a pair is limited to a definite direction irrespective of thedirection of force applied, then the motion is said to be a completely constrained motion. Shaft with collars in a circular hole Square bar in a square holeThe motion of a square bar in a square hole and the motion of a shaft with collars at eachend in a circular hole, are also examples of completely constrained motion.3. 1.2. Incompletely constrained motionWhen the motion between a pair can take place in more than one direction, then themotion is called an incompletely constrained motion. The change in the direction ofimpressed force may alter the direction of relative motion between the pair. A circular baror shaft in a circular hole is an example of an incompletely constrained motion as it mayeither 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 bearing3.1.3. Successfully constrained motion When the motion between the elements, forming a pair, is such that the constrainedmotion is not completed by itself, but by some other means, then the motion is said to besuccessfully constrained motion. Consider a shaft in a foot-step bearing as shown above.The shaft may rotate in a bearing or it may move upwards. This is a case of incompletelyconstrained motion. But if the load is placed on the shaft to prevent axial upwardmovement of the shaft, then the motion of the pair is said to be successfully constrainedmotion. The motion of an I.C. engine valve (these are kept on their seat by a spring) and thepiston reciprocating inside an engine cylinder are also the examples of successfullyconstrained motion.3.2 Classification of Kinematic PairsThe kinematic pairs may be classified according to the following considerations:YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 4. MET 305 MECHANICS OF MACHINES THEORY-13.2.1. According to the type of relative motion between the elements The kinematic pairsaccording to type of relative motion between the elements may be classified as discussedbelow: (a) Sliding pair. When the two elements of a pair are connected in such a way thatone can only slide relative to the other, the pair is known as a sliding pair. The piston andcylinder, cross-head and guides of a reciprocating steam engine, ram and its guides inshaper, tail stock on the lathe bed etc. are the examples of a sliding pair. A littleconsideration 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 thatone can only turn or revolve about a fixed axis of another link, the pair is known as turningpair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journalbearing in an engine, lathe spindle supported in head stock, cycle wheels turning over theiraxles etc. are the examples of a turning pair. A turning pair also has a completelyconstrained motion. (c) Rolling pair. When the two elements of a pair are connected in such a way thatone rolls over another fixed link, the pair is known as rolling pair. Ball and roller bearings areexamples of rolling pair. (d) Screw pair. When the two elements of a pair are connected in such a way thatone 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 waythat one element (with spherical shape) turns or swivels about the other fixed element, thepair 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.3.2.2. According to the type of contact between the elements The kinematic pairsaccording to the type of contact between the elements may be classified as discussedbelow: (a) Lower pair. When the two elements of a pair have a surface contact whenrelative motion takes place and the surface of one-element slides over the surface of theother, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairsand screw pairs form lower pairs. High Friction (b) Higher pair. When the two elements of a pair have a line or point contact whenrelative motion takes place and the motion between the two elements is partly turning andpartly 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 ofhigher pairs. Low FrictionYANBU INDUSTRIAL COLLEGE 1/11/2013
  • 5. MET 305 MECHANICS OF MACHINES THEORY-14. Kinematic ChainA kinematic chain may be defined as a combination of kinematic pairs, joined in such a waythat each link forms a part of two pairs and the relative motion between the links orelements is completely or successfully constrained. For example, the crankshaft of anengine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rodwith the crank forms a second kinematic pair, the piston with the connecting rod forms athird pair and the piston with the cylinder forms a fount pair. The total combination ofthese links is a kinematic chain.5. MechanismWhen one of the links of a kinematic chain is fixed, for transmitting or transforming motionthe chain is known as mechanism. e.g. Engine indicators, typewriter etc. A mechanism withfour links is known as simple mechanism, and the mechanism with more than four links isknown as compound mechanism. When a mechanism is required to transmit power or to dosome particular type of work, it then becomes a machine. In such cases, the various links orelements 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 whicheach part is reduced to the simplest form to transmit the required motion.6. Degrees of freedom (Mobility)The number of degrees of freedom of a linkage is the number of independent parameterswe must specify to determine the position of every link relative to the frame or fixed link.The number of degrees of freedom of a linkage may also be called the mobility of thelinkage. If the instantaneous configuration of a system may be completely defined byspecifying one independent variable, that system has one degree of freedom. Mostpractical mechanisms have one degree of freedom.An unconstrained rigid body has six degrees of freedom: translation in three coordinatedirections and rotation about three coordinate axes. A body that is restricted to motion in aplane has three degrees of freedom: translation in two coordinate directions and rotationwithin the plane.7. Inversion of MechanismWe have already discussed that when one of links is fixed in a kinematic chain, it is called amechanism. So we can obtain as many mechanisms as the number of links in a kinematicchain by fixing, in turn, different links in a kinematic chain. This method of obtainingdifferent mechanisms by fixing different links in a kinematic chain is known as inversion ofthe mechanism.It may be noted that the relative motions between the various links is not changed in anymanner through the process of inversion, but their absolute motions (those measured withrespect to the fixed link) may be changed drastically.YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 6. MET 305 MECHANICS OF MACHINES THEORY-1Note: The part of a mechanism, which initially moves with respect to the frame or fixed linkis called driver and that part of the mechanism to which motion is transmitted is calledfollower. Most of the mechanisms are reversible, so that same link can play the role of adriver and follower at different times. For example, in a reciprocating steam engine, thepiston is the driver and flywheel is a follower while in a reciprocating air compressor, theflywheel is a driver.8. Grashof’s Law. A very important consideration while designing a mechanism to be drivenby a motor, obviously, is to ensure that the input link can make complete revolution.Mechanisms in which no link makes complete revolution would not be useful in suchapplications. For four bar chain there is a simple test of whether this is the case.Grashof’s Law states that, for a planer four-bar linkage, the sum of the shortest and thelongest link length cannot be greater than the sum of the remaining two link lengths, ifthere is a continuous relative motion between two members.9. Types of Kinematic ChainsThe most important kinematic chains are those which consist of four lower pairs, each pair being asliding pair or a turning pair. The following three types of kinematic chains with four lower pairs areimportant from the subject point of view The following three types of kinematic chains withfour 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.These kinematic chains are discussed, in detail, in the following articles.9.1 Four Bar Chain or Quadric Cycle Chain Four bar chainWe have already discussed that the kinematic chain is a combination of four or morekinematic pairs, such that the relative motion between the links or elements is completelyconstrained. The simplest and the basic kinematic chain is a four bar chain or quadric cyclechain, it consists of four links, each of them forms a turning pair at A, B, C and D.9.2 Inversions of Four Bar ChainThough there are many inversions of the four bar chain, yet the following are importantfrom the subject point of view:9.2.1. Beam engine (crank and lever mechanism)YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 7. MET 305 MECHANICS OF MACHINES THEORY-1 Beam engine.Parts of the mechanism of a beam engine (also known as crank and lever mechanism) whichconsists of four links, is shown above. In this mechanism, when the crank rotates about thefixed centre A, the lever oscillates about a fixed centre D. The end E of the lever CDE isconnected to a piston rod which reciprocates due to the rotation of the crank. In otherwords, the purpose of this mechanism is to convert rotary motion into reciprocatingmotion.9.2.2. Coupling rod of a locomotive (Double crank mechanism) Coupling rod of a locomotiveThe mechanism of a coupling rod of a locomotive (also known as double crank mechanism)which consists of four links is shown above. In this mechanism, the links AD arid BC (havingequal length) act as cranks and are connected to the respective wheels. The link CD acts as acoupling rod and the link AB is fixed in order to maintain a constant centre to centredistance between them. This mechanism is meant for transmitting rotary motion from onewheel to the other wheel.9.2.3. Pantograph (Double Lever Mechanism)YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 8. MET 305 MECHANICS OF MACHINES THEORY-1When it is desired to duplicate some motion exactly but to a reduced or enlarged scale,some short of copying device in the form of Pantograph is used. It is basically a quadriccycle chain in the form of a parallelogram.9.2.3. a Indicator mechanism (Double lever mechanism) Watts indicator mechanismA Watts indicator mechanism (also known as Watts straight line mechanism or doublelever mechanism) which consists of four links is shown above. The four links are BCextended to A, CD extended to E, BF and DF. Displacement of the joint F is directlyproportional to the pressure of gas or steam which acts on the indicator plunger. On anysmall displacement of the mechanism, the tracing point E at the end of the link CE tracesout approximately a straight line.The initial position of the mechanism is shown by full lines, whereas the dotted lines showthe position of the mechanism when the gas or steam pressure acts on the indicatorplunger.9.3 Single Slider Crank ChainA single slider crank chain is a modification of the basic four bar chain. It consists of onesliding pair and three turning pairs. It is usually, found in reciprocating steam enginemechanism, this type of mechanism converts rotary motion into reciprocating motion andvice versa.YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 9. MET 305 MECHANICS OF MACHINES THEORY-1 Single slider crank chainThe link 1 corresponds to the frame of the engine, which is fixed. The link 2 corresponds tothe crank link 3 corresponds to the connecting rod and link 4 corresponds to cross-head. Asthe crank rotates, the cross-head reciprocates in the guides and thus the piston reciprocatesin the cylinder.9.4 Inversions of Single Slider Crank ChainWe 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 obtainedand 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 inthe following mechanisms.9.4.1. Pendulum pump or Bull engine Pendulum pumpIn this mechanism, the inversion is obtained by fixing the cylinder or link 4 (i.e. sliding pair), asshown. In this case, when the crank (link 2) rotates, the connecting rod (link 3) oscillatesabout 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 pistonsattached to link 1. YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 10. MET 305 MECHANICS OF MACHINES THEORY-19.4.2. Oscillating cylinder engineThe arrangement of oscillating cylinder engine mechanism, as shown in Fig. 5.24, is used toconvert reciprocating motion into rotary motion. In this mechanism, the link 3 forming theturning pair is fixed. The link 3 corresponds to the connecting rod of a reciprocating steamengine mechanism. When the crank (link 2) rotates, the piston attached to piston rod (link1) reciprocates and the cylinder (link 4) oscillates about a pin pivoted to the fixed link at A.9.4.3. Rotary internal combustion engine or Gnome engine Sometimes back, rotary internal combustion engines were used in aviation. But now-a-daysgas turbines are used in its place. It consists of seven cylinders in one plane and all revolvesabout fixed centre D, as shown in Fig. 5.25, while the crank (link 2) is fixed. In thismechanism, when the connecting rod (link 4) rotates, the piston (link 3) reciprocates insidethe cylinders forming link 1 Rotary internal combustion engine.YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 11. MET 305 MECHANICS OF MACHINES THEORY-19.4.4. Crank and slotted lever quick return motion mechanism. Crank and slotted lever quick return motion mechanismThis mechanism is mostly used in shaping machines, slotting machines and in rotary internalcombustion engines. In this mechanism, the link AC (i.e. link 3) forming the turning pair isfixed. The link 3 corresponds to the connecting rod of a reciprocating steam engine. Thedriving crank CB revolves with uniform angular speed about the fixed centre C. A slidingblock attached to the crank pin at B slides along the slotted bar AP and thus causes AP tooscillate about the pivoted point A. A short link PR transmits the motion from AP to theram, which carries the tool and reciprocates along the line of stroke. The line of stroke ofthe ram is perpendicular to AC produced.In the extreme positions, AP1 and AP2 are tangential to the circle and the cutting tool is at theend of the stroke. The forward or cutting stroke occurs when the crank rotates from theposition CB1, to CB2 (or through an angle β) in the clockwise direction. The return stroke occurswhen the crank rotates from the position CB2 to CB1, (or through angle α) in the clockwisedirection.YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 12. MET 305 MECHANICS OF MACHINES THEORY-1 . Whitworth quick return motion mechanism9.4.5 Whitworth quick return motion mechanismThis mechanism is mostly used in shaping and slotting machines. In this mechanism, the link CD(link 2) forming the turning pair is fixed. The link 2 corresponds to a crank in a reciprocatingsteam engine. The driving crank CA (link 3) rotates at a uniform angular speed. The slider (link4) attached to the crank pin at A, slides along the slotted bar PA (link 1) which oscillates at apivoted point D. The connecting rod PR carries the ram at R to which a cutting tool is fixed. Themotion of the tool is constrained along the line RD produced, i.e. along a line passing through Dand perpendicular to CD.When the driving crank CA moves from the position CA1 to CA2 (or the link DP from positionDP1 to DP2) through an angle a in the clockwise direction, the tool moves from the left handend 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 DP2toDP1) through an angle β in the clockwise direction, the tool moves back from right hand end ofits stroke to the left hand end.A little consideration will show that the time taken during the left to right movement of theram (i.e. during forward or cutting stroke) will be equal to the time taken by the driving crankto move from CA1 to CA2. Similarly, the time taken during the right to left movement of theram (or during the idle or return stroke) will be equal to the time taken by the driving crank tomove from CA2 to CA1Since the crank link CA rotates at uniform angular velocity therefore time taken during thecutting stroke (or forward stroke) is more than the time taken during the return stroke. In otherwords, the mean speed of the ram during cutting stroke is less than the mean speed during thereturn stroke.YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 13. MET 305 MECHANICS OF MACHINES THEORY-19.5. Double Slider Crank ChainA kinematic chain which consists of two turning pairs and two sliding pairs is known as doubleslider crank chain.. We see that the link 2 and link 1 form one turning pair and link 2 and link 3form the second turning pair. The link 3 and link 4 form one sliding pair and link 1 and link 4form the second sliding pair.9.6. Inversions of Double Slider Crank ChainThe following three inversions of a double slider crank chain are important from the subjectpoint of view:9.6.1. Elliptical trammels. It is an instrument used for drawing ellipses. This inversion isobtained by fixing the Slotted plate (link. 4), as shown .A. The fixed plate or link 4 has twoStraight grooves cut in it, at right angles to each other. The link 1 and link 3, are known assliders and form sliding pairs with link 4. The link AB (link 2) is a bar which forms turning pairwith links 1 and 3. When the links 1 and 3 slide along their respective grooves, any point on thelink 2 such as P traces out an ellipse on the surface of link 4, as shown below. A littleconsideration will show that AP and BP are the semi-major axis and semi-minor axis of theellipse respectively. Elliptical trammelsYANBU INDUSTRIAL COLLEGE 1/11/2013
  • 14. MET 305 MECHANICS OF MACHINES THEORY-1 Scotch yoke mechanism9.6.2. Scotch yoke mechanism This mechanism is used for converting rotary motion into areciprocating motion. The inversion is obtained by fixing either the link 1 or link 3. The link 1 isfixed. In this mechanism, when the link 2 (which corresponds to crank) rotates about B ascentre, the link 4 (which corresponds to a frame) reciprocates. The fixed link 1 guides theframe.9.6.3. Oldhams coupling An Oldham’s coupling is used for connecting two parallel shaftswhose axes are at a small distance apart. The shafts are coupled in such a way that if one shaftrotates, the other shaft also rotates at the same speed. This inversion is obtained by fixing thelink 2, as shown below. The shafts to be connected have two flanges (link 1 and link 3) rigidlyfastened at their ends by forging. Oldhams couplingThe link 1 and link 3 form turning pairs with link 2. These flanges have diametrical slotscut in their inner faces, as shown in Fig. (b). The intermediate piece (link 4) which is acircular disc, have two tongues (i.e. diametrical projections) T1 and T2 on each face atYANBU INDUSTRIAL COLLEGE 1/11/2013
  • 15. MET 305 MECHANICS OF MACHINES THEORY-1right angles to each other, as shown in Fig (c). The tongues on the link 4 closely fit intothe slots in the two flanges (link 1 and link 3). The link 4 can slide or reciprocate in theslots in the flanges.When the driving shaft A is rotated, the flange C (link 1) causes the intermediate piece(link 4) to rotate at the same angle through which the flange has rotated, and it furtherrotates the flange D (link 3) at the same angle and thus the shaft B rotates. Hence links1, 3 and 4 have the same angular velocity at every instant. A little consideration willshow, that there is a sliding motion between the link 4 and each of the other links 1 and3.If the distance between the axes of the shafts is constant, the centre of intermediatepiece will describe a circle of radius equal to the distance between the axes of the twoshafts. Therefore, the maximum sliding speed of each tongue along its slot is equal tothe peripheral velocity of the centre of the disc along its circular path.YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 16. MET 305 MECHANICS OF MACHINES THEORY-1right angles to each other, as shown in Fig (c). The tongues on the link 4 closely fit intothe slots in the two flanges (link 1 and link 3). The link 4 can slide or reciprocate in theslots in the flanges.When the driving shaft A is rotated, the flange C (link 1) causes the intermediate piece(link 4) to rotate at the same angle through which the flange has rotated, and it furtherrotates the flange D (link 3) at the same angle and thus the shaft B rotates. Hence links1, 3 and 4 have the same angular velocity at every instant. A little consideration willshow, that there is a sliding motion between the link 4 and each of the other links 1 and3.If the distance between the axes of the shafts is constant, the centre of intermediatepiece will describe a circle of radius equal to the distance between the axes of the twoshafts. Therefore, the maximum sliding speed of each tongue along its slot is equal tothe peripheral velocity of the centre of the disc along its circular path.YANBU INDUSTRIAL COLLEGE 1/11/2013
  • 17. MET 305 MECHANICS OF MACHINES THEORY-1right angles to each other, as shown in Fig (c). The tongues on the link 4 closely fit intothe slots in the two flanges (link 1 and link 3). The link 4 can slide or reciprocate in theslots in the flanges.When the driving shaft A is rotated, the flange C (link 1) causes the intermediate piece(link 4) to rotate at the same angle through which the flange has rotated, and it furtherrotates the flange D (link 3) at the same angle and thus the shaft B rotates. Hence links1, 3 and 4 have the same angular velocity at every instant. A little consideration willshow, that there is a sliding motion between the link 4 and each of the other links 1 and3.If the distance between the axes of the shafts is constant, the centre of intermediatepiece will describe a circle of radius equal to the distance between the axes of the twoshafts. Therefore, the maximum sliding speed of each tongue along its slot is equal tothe peripheral velocity of the centre of the disc along its circular path.YANBU INDUSTRIAL COLLEGE 1/11/2013