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# Kinematics of machines Question Papers

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### Kinematics of machines Question Papers

1. 1. ll"!1 06ME44 USN Fourth semester B.E. Degree Examination, I)ecemb er 2oll Kinematics of Machines Max. Marks:100 Time: 3 hrs. Note: Answer any FIW full questions, selecting at least TWO questions ftom eaeh part Ci o PART -A o d o. I a. Define the following, with sketches: (08 Marks) (! i) Link Mechanism iii) Machine iv) Inversion. ii) ad c) b. Explain: i) Lower pairs ii) Higher pairs (06 Marks) an inversion of a slider c) c. Describe with a neat sketch, the crank and slotted lever mechanism, (06 Marks)B9 crack mechanism&. neat sketch (10 Marks)d9 2 a. Explain the Whitworth quick return motion mechanism, with a Explain with a neat sketch, b. Derive the expression for necessary condition of correct steering. lloo d6,=+ (10 Marks).EN the Ackerman steering gear mechanismbip and connecting otr-c !l 3 A single slider crank mechanism shown in Fig.Q3, has the crank cB = 100rnm has a speed of oF rod BA : 300;, with eeatre of gravity G-ld0mm ftom B. The crankshaft3s 75 radlsecand an angular acceleration of 1200 rad/sec. Find@(d i) The velocityof G and the angular velocrty of AB bE ii) The acceleiation of G and angular acceleration of AB. (20 Marks) do 6 ot o0g d.d >e 26 6r oP Fis.Q3 Locate all the instantaneous centres ano frna *re angular velocity of the link BC The link -O qo- tro. 4 a. and AD:600mm o.. oi dimensions of the mechanism are AB = 300mm, BC = BD:360mm The angle BAD :60". The crank rotates at 100 rpm.lRefer Fig.Qa(\$l (10 Marks) o.|: }U olt 6E r() coo coo ar= o. iB Fig.Qa(a) tr> =o 3L engine are 200mm and -> ,J< b. The lengths of the crank and the connecting rod o{ a reciprocating 120 rad/sec when the -i oi 700mm r"rpr.rir"ly. rrr. crank rotates in clockwise direction at c) crank is at 30oC toiDC, by using the Kleins construction, determine and acceleration of the cR i) The velocity *a u..*f*ration Jf the piston ii)Angular velocity o Z (10 Marks) o. 1 of2
2. 2. a 06ME44 PART -B The crank and connecting rod of an engine are 0.3m and 1.5 in length respectively.The crank rotates at 180 rpm clockwise. Determine the velocity and acceleration of the piston when the crank is 40o from TDC. Also determine the position of the crank for zero acceleration of the piston. (20 Marks) 6 a. Derive the expression for the length of arc of contact in a pair of spur gears in a mesh. (08 Marks) b. Two mating gears have 20 and 40 involute teeth of module 10mm and 20o pressure angle. The addendum of each wheel is to be made of such a length that the line of contact on each side of the pitch point has half the maximum possible length. Determine the addendum length for each wheel, length of path of contact, arc of contact and contact ratio. (12 Marks) 7 a. Explain with a neat sketch the oSun & planet wheel" (04 Marks) b. In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth, respectively. If the arm rotates at 150 rpm in the anticlockwise direction about the centre of gear A which is fixed, determine the speed of the gear B, if the gear A instead of being fixed, makes 300 rpm in the clockwise direction. [Refer Fie.Q7(b)]. (16 Marks) Ag Fie.Q7(b) 8 Construct the profile of a cam to suit the following specifications: Cam shaft diameter = 40mm Least radius of cam:25mm Diameter of the roller:25mm - Angle of lift 120" : Angle of fall 150" Lift of the follower = 40mm No. of pauses are two of equal interval between motion. During the lift the motion is SHM. During the fall motion is UARM. The speed of camshaft is uniform. The line of stroke is offset to 12.5mm from the centre of the cam. (20 Marks) *!t*!*rk 2 of2
3. 3. r 06M.E,44 Fourth Semester B.E. Degree Examination, June/July 201,1 Kinematics of Machines Time: 3 hrs. Max. Marks:100 Note: Answer any FIVEfull questions. selecting atleast TWO from each.parl. .: 2 PART -A I a. Define: i) Kinematic chain 2 ii) Machine E iii) Structure iv) Self closed pair v) Force closed pair. (10 Marks) ; b. Sketch and explain any two inversions of four bar chain. (10 Marks) (,e ll oo troo ,!N Sketch and explain the following : dt HoO a. Whitworth quick return mechanism. (08 Marks) ts(.) Ratchet and pawl mechanism. (08 Marks) otr -co b. c. Toggle mechanism. (04 Marks) a7 !L u.d A four bar chain of links PQ, QR and RS are 62.5 mm, 175 mm ancl 120 mm long respectively, the link PS of chain PQRS is fixed and having iength of 200 mm. The link PQ bU makes an angle of 60" rvith PS and rotaies at i0 radl sec ciockwise. Detennine : 6O BOE i) Angular veiocity of links QR and RS ii) Angular acceleration,:f link QR and RS. (20 frIarks) ;ts s6J 4 a. In a reciprocating engine the length of crank is 250 mm and length of connecting rod is 1000 mm. The crank rotates an uniform speed of 300 rpm. Determine the velocity and 3 = ;i acceleration of piston, when the crank is 30 from inner dead centre, use Kleins tro. construction" (l0lVlarks) o" o-a b. Locate all instantaneous benters for the following mechanism. (10 Marks) ao @ lE L (,) a,- >h bo troo (J= uo tr> :() 5E (r< Fie. Qa&)(ii) Fig. Qa@Xi) -i .i O o PART B z - o. 5a. Explain the significance of loop closure equation, with example. (05 Marks) b. The crank of an engine mechanism is 200 mm long and the ratio of connecting rod length to the crank radius is 4. Determine the acceleration of the piston when crank has turned through an angle 45o from inner dead centre and rotatin g at a speed of 240 rpm counter clockwise direction by complex number approach. (15 Marks) I of2
4. 4. 06M8446a. What is interference in involute gears? Derive an expression for the length of arc of contact in a pair of meshed spur gears. (10 Marls) b. Two gear wheels mesh externally and are to give a velocity ratio of 3 to 1. The teeth are of involute form module:6 mm, addendum: one module, pressure angle = 20". The pinion rotates at 90 rpm. Determine : i) Minimum no. of teeth on each wheel to avoid interference ii) The number of pair of teeth in contact. (10 Marlis) An epicyclic gear train consist of a sun wheel S, a stationary intemal gear E and three identical planet wheels P carried on a stat- shape planet carrierC. The size of difterent toothed wheels are such that the planet carrier C rotates one revolution for every 5 revolutions of the sun wheel S. The minimum number of teeth on any wheel (say P) is 16. the driving torque on the sun wheel is 100 N -m. Determine i) Number of teeth on different wheels of the train. ii) Toque necessary to keep the internal gear stationary. (20 Marls) Fig. Q7 The following data relate to cam profile in which the roller follower moves with SHM during ascent and uniform acceleration and retardation motion during descent. Minimum radium of cam :30 mm Roller radius :8 mm Lift =28mm Offset of follower axis : 12 mm towards right Angle of ascent :90" Angle of descent :60o Angle of dwell between ascent and descent :45o Speed ofcam :200 rpm Draw the profile of cam and determine the maximum verocitv and acceleration during outstroke and return stroke. (20 Marks) ***** 2 of2
5. 5. USN 06M844 Fourth Semester B.E. Degree Examination, Dec.08 / Jan.O9 Kinematics of MachinesTime: 3 hrs. Max. Marks:100 Note : Answer any FIVE questions selecting ot least two from each part. Part A a. Define with suitable examples : i) Structure ii) Machine iii) Mechanism iv) Higher pair (08 Marks) b. Sketch and explain the following: i) Beam engine ii) Gnome engine. iii) Ellipticaltrammel. (12 Marks) a. Sketch the crank and slotted lever mechanism. Indicate the (06 Marks) strokes. b. Sketch and explain Geneva wheel mechanism. (07 Marks) c. Sketch Ackremann steering mechanism and obtain condition for correct steering. (07 Marks) A double slider crank mechanism is shown in figure Q3. The crank OA rotates at a constant angular velocity of 10 radlsec. The links OA, AB and AC are 100 mm, 200mm and 200 mm long respectively. By drawing the velocity and acceleration polygons determine: a. Velocity and acceleration of each slider. b. Angular velocity and angular acceleration of each connecting rod. (20 Marks) -+I ,,.!, a. .-. ..--/ .c112--a- - 4 .7..," ?. ,. .a r10 l/ - * !f- 1 - ,+i f o-l-r I Fig. Q3 Locate all the instantaneous centers for a i) Four bar mechanism. ii) Slider crank mechanism. (10 Marks) b. Determine the velocity and acceleration of the piston by Kleins construction for a steam engine to the following specifications: Stroke of piston: 600 mm Ratio of length of connecting rod to crank length:5 Speed of engine:450 rpm clockwise. Position of crank: 45" with inner dead centre. (10 Marks) 1 of ?
6. 6. 06M.F,44 obtain loop closure equation ro, u +-u*P,f,.ltn?oir*. (04 Marks) Develop equations for the angular velocities and angular accelerations for the links 3 and 4 as shown in figure Q5 O) using complex algebra method. ,tr, (16 Marks) ,t *-* r-" -j g l 63 I ?-.. ,d / b.L h I , l/1 , 1,. t0r , *[---- I d, ^n Fig. Qs (b)a. cornpare cycloidal and involute gear tooth profile. (05 Marks)b. What is rneant by interference? Mention various methods of avoiCing interference in gears. Two gear wheels have respectively 28 and45 teeth and a standard aaaenoullsf;Tl module. The pressure angle is 20" and the module of 6 mm Determine : i) length of path of contact. ii) contact ratio. (i0 Marks) Sketch and explain: i) Simple gear train. ii) Epicyclic geartrain. (06 Marks) In an epicyclic gear train of sun and planet type, the pitch circle diameter of the Annular wheel (A) is 425 mm and the module is 5 mm" When the annular wheel is stationary, the spider which carries 3 planet Gears (P) of equal size has to make one revolution for every d revolutions of the driving spindle carryrng sun wheel (S). Determirte the number of teeth on all the wheels. (I,l Marks)Draw the profile of a cam operating a roller reciprocating foilower and with the following : :data: Minimum radius of cam 25 mm, Lift 30 mm; Rolter diameter 15 mm. The cam lifti :the follower for 120 with SHM followed by a dweil period of 30", then the follower lcwersdown during 150" of the cam rotation with UARM followed by a dwell period. The camrotates at a uniform speed of 150 rprn (CW direction). The axis of the follower passes throughthe axis of the cam shaft. Calculate the maximum velocity and acceleration of the followerduring the descent period. (20 Marks)
7. 7. ME44uix July 08 Fourth semester B.E. Degree Examination, June / Kinematics of Machines Max. Marks:100 Time:3 hrs- Note Answer any FIVE full questions z1^. 2. Graphieai questions can be drawn oru drawing sheet 3. Miising data if any may be suitably assumed Differentiate between: i) Lower pair and higher pair ii) Machine and mechanism 1a. (05 Marks) iiD Constrained and unconstrained motion the entarged or b. Jil;;JJ ffiffiire working of pantffih and prove that it reproduces (08 Marks) reduced size drawings. (06 Marks) yoke mechanism Sketch and explain tle working of scotch (08 Marks) mechanisms: 2a. Find the degrees of freedom for the following Fig. Q2 (a) slider mechanism b. With neat sketches explain the working of all the inversit,.ns of dcuble (12 Marks) find for the given If the crank OA rotates at 150 rpm in the antislockwise direction, I) (20 Marks) tnfiguration the velocity and accelerdtion of slider B and t K--1€Orayp, -{ OA: 80 mm AC: CB : CD = 120 mm Fig. Q3 t of2
8. 8. M.E444a. state and prove Arnold-Kennedys theorem. (05 Marks) b. Locate all the instantaneous centers of the mechanism shown. Find the angular velocity of link AB. oA:200 mm, AB: 1500 mrn, BC:600 mm, cD:500 *m urrd BE:400 mm. OA rotates at 120 rpm clockwise. (15 Marks) - r: Fig. Qa &)Ja- Derive an expression for loop closure equation for four bar mechanism. (08 Marks) b. If the crank and connecting rod are 150 mm and 600 mm long respectively and the crank rotates at constant speed of 100 rpm, determine i) Velocity and acceleration of piston and ii) Angular velocity and angular acceleration of connecting rod. The angle, which the crank makes with the inner dead centre, is 30". (12 Marks)6a. Explain and derive the condition for the law of gearing. (08 Marks) b. A pinion having 30 teeth drives a gear having 80 teeth. The profile of the gears is involute with 20 pressure angle, 12 mm module and 10 mm addendum. Find the length of path of contact, arc ofcontact and contact ratio. (12 Marks) Figure shows diagrarnmatically a compound epicyclic gear train. Wheels A, D and E are free to rotate independently on spindle O, while B and C are cornpound and rotate together on spindle P, on the end of arm OP. All the teeth of different wheeli have same module. A has 12 teeth, B has 30 teeth and C has 14 teeth cut externally. Find the number of teeth on wheels D and E, which are cut internally. If the wheel A is driven clockwise at 1 rps while D is driven counterclockwise at 5 rps, determine the magnitude and direction of angular velocities of arm OP and wheel E. (20 Marks) Fig. Q7 Construct the profile of a cam to suit: Cam shaft diameter : 40 mm; Least radius of cam : 25 mm; Diameter of roller : 25 mm; Angle of lift :120: Angle of fall: 150"; Lift of the follower: 40 mm;Number of pauses are two of equal interval between motions. During the lift the motion is SHM. During the fall the motion is uniform acceleration and deceleration. The speed of the camshaft is uniform. The line of stroke of the follower is oflset 12.5 mm from the centre of the cam. (20 Marks)
9. 9. t *F ui* ME44 Fourth semester B.E. Degree Examination, Dec. 07 / Jan. 08 Kinematics of Machines Time:3 hrs. Max. Marks:100 Note z T.Answer any FIVEfull questions 2.Graphicalsolutionscanbedrawnondrawingsheet. a. Distinguish between : pair. i) Complete constraint and successful constraint ii) Open pair and closed iii) Structure and kinematic chain iv) Ivlechanism and machine. (08 Marks) b. Explain with neat sketches, three inversions of double slider crank chain. (12 Marks) With neat proportionate diagrams explain the principle and working of following mechanisms a. Whitworth mechanism b. Geneva mechanism c. Toggle mechanism (20 Marks) d. Hookes joint. The Fig.3 shows Roberts straight line mechinism in which pointCmoves.in ahorizontal and its velocity and direction. 02 and O+ are tlie fiied points. pzA is a crank 75 mm long acceleration are Z0 rad./sec and 100 rad/secz respectively, both clockwise. The dimensions of : other links are : AB :75 mm, o+B 75 mm, lozo 4 = 45o, OzO+: 125 mm. The pointc traces its path along horizontal line .joininB OzO+. Find the velocities and accelerations of point C and link O+ B. Fig.3 (20 Marks) The mechanism of a wrapping machine, is as shown in Fig4 has the following dimensions: OrA: 100 mm; AC : 700 mm; BC :200 mm; O:C :200 mm; OzE:400 mm; OzD:200 mm and BD: 150 mm the velocity of the The crank OrA rotates at uniform angular velocity of 100 rad/sec. Find point E of the bell crank iever by instantaneous centre method. € 1?r i, !6 ti 1 r,i ,srTZ -:r*J- I I 1 i!c.c nLw l Fc-i -- Fig.4 (20 Marks) I of2
10. 10. ME+4 Use kineuatic analysis of the slider- crank by complex numbers and derive the expressions 9rveJ99ttrandaccelerationoftheslider*d.o*i.tingrod.]--_- The slider-crank of an internal combustion engine shoil in Fig.s(b) includes a crank of 50.8 mm tength and a connecting rod of 203 rin length. Th...rril;p;;J;f;;;*;;; f,gl;f ,h.;"#.;G constant at 314 rad/s. Determine the acceleration of tf,e *uss r.ri.. rod when &e crank angle is 30o. The mass centre at A. 93 is located 50.8*J rro", ifr. crank pin Fig.s(b) (10 Marks)6a. what is meant by involute irrtrrr"r.n"lrgJ(o b. Derive * for the minimum number of teeth on a pinion mating *rh(:r[[T: avoid interference. "*pr"rrion (06 Marks) c. Two mating involute gears of 20o pressure angle have a gear ratio of 2. The number of teeth on pinion is 20. The speed of pinion is 250 rpm. Takeirodule as l2 mm. If the addendum on each wheel is such that the path of approach and path of recess on eaeh side are of half the maximum possible length each; find: i) The addendum of pinion and gear ii) The l."gth of*, of contact. (r0 Marks) a. The FigT shows an epicyclic gear train. Pinion A has 15 teeth and is rigidly fxed in the motor shaft- The wheel B has 20 teeth and gears with A and also with aniular fixed wheel D Finion C has 15 teeth qd it integral with B (C and B being a compound wheel). Gear C meshes with annular wheel E, which is keyed to the machine shaft. The arm rotates about the same shaft on which A is fixed and carries the compound wheel B runs at 100 rpm, find the speed of the machine shaft. Find also - C. If the motor the torque exerted on the machine shaft if the motor develops a torque of 100 N_m. Fig.7 (20 Marks) Draw the profile of the cam for the following details : a. Minimun radius of the cam -20 mm. b. Rotation-counter clock-wise at 1000 rpm. c. Oufward stroke - UARM l}0o. - d. Follower- l0 mm dia roller. e. Lift ofthe follower- 20 mm. f. Dwell at tull lift - 60o. g. Retum stroke - SHM during 120o. h. offset - foltrower axis 5 mm to the right of the aris of cam. calculate the maxim,m acceleration during retum stroke. (20 Marks) 2 of2
11. 11. -: tr. . Page No... I NIT,44 USN NBW SCHEME Fourth Semester B.E. Degree Examination, July 2007 Mechanical Engineerin g Kinematics of Machines Time: 3 hrs.l [Max. Marks:i00 Note : Answer any FIVE full questions. I a. Define a kinematic chain. Describe various forms of kinematic chain with examples. (05 Marks) b. Explain the Grublers mobility equation for a planar mechanism. Determine the mobility of a cam with an oscillating follower fitted with a roller. (05 Marks) c. Sketch and explain the kinematic chain with three lower pairs. (05 Marks) d. Sketch and explain the elliptical trammel mechanisrn. (05 Marks) 2 a" What is meant by quick-return mechanism? Sketch and explain drag link mechanism" (06 Marks) b. Sketch and explain Peaucellier straight line motion mechanism. (06 Marks) c. A Hookes joint is used to connect two shafts whose axes are inclined at 200. The driving shaft rotates uniformly at 6000 rpm. What are the extreme angular velocities of the driven shaft? Find the maximum value of acceleration and state the angle at which it will occur? (08 Marks) 3 A double slider-crank rnechanism is shown in Fig.3(a). The crank OA rotates at constant angular velocity of 10 radlsec. The links OA, AB and AC are 100 mm, 200 mm and 200 mm long respectively. By drawing the velocity and acceleration polygons, determine : a. Velocity and acceleration of each slider, (10 Marks) b" Angular velocity and angular acceleration of each connecting rod" A Fig.3(a) (20 Marks) The stroke of,a steam engine is 400 mrn and the length of the connecting rod is 600 mm. The crank roJates at 300 rpm clockwise direction and the crank is inclined at 300 with the inner dead center. The center of gravity of the connecting rod is 240 mm away from the crank end. By Kleins construction determine the following : a. Velocity and acceleration of the piston. b. Angularvelocity and angular acceleration of the connecting rod. c. Velocity and acceleration at the center of gravity of the connecting rod. (20 Marks) Contd.... 2
12. 12. Page No... 2 MEl41 -; .Y: . An internal combustion engine has a crank of 150 mm length and a connecting rod of 600 mm length. The crank rotates at a constant speed of 300 rpm counter clockwise. Determine the position, velocity and acceleration of the slider when the crank angle is 450 Iiom the inner dead center position by complex algebra. (20 Marks) a. TIie thickness of an involute gear tooth is 4.98 mm at a radius of 50.8 mm and a pressure angle of 200. Calculate the tooth thickness on the base circie. (05 Marks) b. The foilowing data refer to the two mating involute gears of 200 pressure angle : Number of teeth on pinion is 30, gear ratio is 2, module is 12 mm and the speed of the pinion is 600 rpm. The line of contact on each side of the pitch point is half the maximum possible length. Find the height of addendum for each gear wheel and the length of arc of contact. Also find the maximum velocity of sliding during approach and excess. (15 Marks) la. Sketch and describe a bevel gear differentiaL used in automobiles. (06 Marks) b. A fixed annular gear A and a smaller concentric rotating gear B are connected by a compound gear CD. The gear C mesh with gear A and D with B. The compound gears revolved in a pin on the arm R, which revolves about the axis of A and B. The number of teeth on gears A, B and D are 150, 40 and 100 respectively. Determine the number of teeth on gear C, if the gears A and C have twice the module of gears B and D. How many revolutions will B make for one complete revolution of the arm R? (14 Marks) A cam with a base circle radius of 35 mm is rotating at a uniform speed of 100 rpm in anti-slockwise direction. Draw the profile for the disc cam with reciprocating knife edge follower on the center line of the cam shaft for the following follower motion. a. Follower to move upward 3C mm with simple harmonic rnotion in 0.1 sec. b. Follower to dwell in next 0.15 sec. c. Follower to move upward to another 30 mm uith simple harmonic rnotion in 0.15 sec. d. Follower to return to its starting position with uniform acceleration and retardation in the remaining period of one complete revolution of the cam shaft. However, the acceleration period is twice the retardation period. Determine the maximum velocity and acceleration of the follower during its outward stroke. (20 Marks) JgJJC