GUJARAT TECHNOLOGICAL UNIVERSITY PDF Winter 2022 Past Exam Paper

Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER– III(NEW) EXAMINATION – WINTER 2022 Subject Code:3131906 Date:27-02-2023 Subject Name...

Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER– III(NEW) EXAMINATION – WINTER 2022 Subject Code:3131906 Date:27-02-2023 Subject Name:Kinematics and Theory of Machines Time:02:30 PM TO 05:00 PM Total Marks:70 Instructions: 1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. 4. Simple and non-programmable scientific calculators are allowed. Marks Q.1 (a) Differentiate Lower pair and Higher Pair 03 (b) Classify different types of constrained motions. 04 (c) Draw and explain Peaucellier mechanism and 07 Q.2 (a) Classify different types of cams according to types of shape. 03 (b) Classify and draw different follower displacement diagram. 04 (c) Two involute gears of 20° pressure angle are in mesh. The number of teeth on pinion is 07 20 and the gear ratio is 2. If the pitch expressed in module is 5 mm and the pitch line speed is 1.2 m/s, assuming addendum as standard and equal to one module, find the angle turned through by pinion when one pair of teeth is in mesh and the maximum velocity of sliding. OR (c) Construct cam profile for knife edge follower with offset to right by 15 mm. Minimum 07 radius of the cam = 30 mm, stroke of the follower = 24 mm. angle of rise = 90O, dwell after rise = 60O, angle of return = 120O, dwell after return for the rest of the period. Follower move outward with uniform velocity and return back with simple harmonic motion. The cam is rotating in clockwise direction. Q.3 (a) Explain the term coupler curves. 03 (b) Explain chebychev spacing method 04 (c) A four-bar chain mechanism is to be designed by using three precision points to generate 07 the function Y = X 1.5 for the angle range 1 ≤ x ≤ 4. Assuming 30O starting position and 120O finishing position for the input link and 90O starting position and 180O for finishing position for the output link, find the value of x, y, θ, Φ corresponding to three precision point. OR Q.3 (a) State the law of gearing. 03 (b) Differentiate spur and helical gear. 04 (c) In a reverted epicyclic gear train, the arm A carries two gears B and C and a compound 07 gear D - E. The gear B meshes with gear E and the gear C meshes with gear D. The number of teeth on gears B, C and D are 75, 30 and 90 respectively. Find the speed and direction of gear C when gear B is fixed and the arm A makes 100 r.p.m. clockwise. 1 Q.4 (a) Explain klein's construction. 03 (b) Explain the term rubbing velocity. 04 (c) The mechanism of a machine, as shown in Figure, has the following dimensions: O1A = 07 100 mm, AC = 700 mm, BC = 200 mm, O3C = 200 mm, O2E = 400 mm, O2D = 200 mm and BD = 150 mm. The crank O1A rotates at a uniform speed of 100 rad/s. Find the velocity of the point E of the bell crank lever by instantaneous center method. OR Q.4 (a) State and explain aronhold- kennedy theorem. 03 (b) Explain angular velocity, linear velocity, angular acceleration and linear acceleration. 04 (c) Figure shows configuration of an engine mechanism. The dimensions are the following: 07 Crank OA = 200 mm; Connecting rod AB = 600 mm; distance of center of mass from crank end, AD = 200 mm. At the instant, the crank has an angular velocity of 50 rad/s clockwise and an angular acceleration of 800 rad/s2. Calculate the (i) velocity of D and angular velocity of AB (ii) acceleration of D and angular acceleration of AB Q.5 (a) State the law of belting 03 (b) Compare belt drive, rope drive and chain drive. 04 (c) In an open-belt drive, the diameters of the larger and the smaller pulleys are 1.2 m and 07 0.8 m respectively. The smaller pulley rotates at 320 rpm. The center distance between 2  the shafts is 4 m. When stationary, the initial tension in the belt is 2.8 kN the mass of the belt is 1.8 kg/m and the coefficient of friction between the belt and the pulley is 0.25. Determine the power transmitted. OR Q.5 (a) Classify the different type of brakes. 03 (b) Explain the working of multi plate clutch with neat sketch. 04 (c) A rope drive transmits 600 kW from a pulley of effective diameter 4 m, which runs at a 07 speed of 90 r.p.m. The angle of lap is 160°; the angle of groove 45°; the coefficient of friction 0.28; the mass of rope 1.5 kg / m and the allowable tension in each rope 2400 N. Find the number of ropes required. 3  C. K. Pithawala College of Engineering and Technology Mechanical Engineering Department Mid Semester Examination [Winter- 2022] B.E. 2nd Year, Semester 3rd semester Subject Code: 3131906 Date: 03-01-2023 Subject Name: Kinematics and Theory of Machine Time: 1:15 Hour Total Marks: 30 Instructions: 1. All questions are compulsory. 2. Figures to the right indicate full marks. 3. Make suitable assumptions wherever necessary. Questionnaires M B.T. CO’s Q:1 (a) Explain Freudenstein’s equation. 03 Und. CO3 (b) Define the following term related to synthesis: 07 U CO3 1. Type synthesis 2. Number synthesis 3. Dimensional synthesis 4. Function generation 5. Path generation 6. Body guidance 7. Synthesis of Mechanism OR (b) A four bar mechanism is to be designed, by using three precision points, to 07 Und. CO3 generate the function y = x1.5 , for the range 1 ≤ x ≤ 4 Assuming 30° starting position and 120° finishing position for the input link and 90°starting position and 180° finishing position for the output link, find the values of x, y, θ and φ corresponding to the three precision points. Q:2 (a) Define: Pitch circle Diameter, Addendum, Dedendum 03 Und. CO2 (b) Classify Gears. 07 E CO2 OR (b) The number of teeth on each of the two equal spur gears in a mesh is 40. The 07 E CO2 teeth have 20◦involute profile and the module is 6 mm. If the arc of contact is 1.75 times the circularpitch, find the addendum. Q.3 (a) Explain friction 03 Und CO5 (b) Explain : 07 U CO5 1. Types of Friction 2. Law of Friction 3. Coefficient of Friction OR (b) Explain the efficiency of Motion up the plane 07 U CO5 M : Marks, B.T. - Blooms of Taxonomy, Und. – Understand, An: Analyze, A: Apply, E = Evaluate, C = Create, CO: Course Objective  C. K. Pithawala College of Engineering and Technology Mechanical Engineering Department Mid Semester Examination [Winter- 2021] B.E. 2nd Year, Semester 3rd semester Subject Code: 3131906 Date: 28-10-2021 Subject Name: Kinematics and Theory of Machine Time: 1:15 Hour Total Marks: 30 Instructions: 1. All questions are compulsory. 2. Figures to the right indicates full marks. 3. Make suitable assumptions wherever necessary. Questionnaires M B.T. CO’s Q:1 (a) Distinguish between: 03 Und. CO1 1. Mechanism & machine 2. Lower & higher pairs 3. Machine & Structure (b) Sketch and describe the working of ONE type of quick return mechanisms. 07 CO1 OR (b) Sketch and explain any ONE inversions of a double slider crank chain. 07 Und. CO1 Q:2 (a) Define 1. Module 2. Pitch 3. Addendum 03 Und. CO2 (b) In a reverted epicyclic gear train, the arm F carries two wheels A and D and a 07 E CO2 compound wheel B, C. The wheel A meshes with wheel B and the wheel D meshes with wheel C. ZA=80, ZD=48 and ZC=72. Find the speed and direction of wheel D when wheel A is fixed and arm F makes 240 rpm clockwise. OR (b) State and prove the “Law of gearing” 07 Und. CO2 C. K. Pithawala College of Engineering and Technology Mechanical Engineering Department Mid Semester Examination [Winter- 2021] B.E. 2nd Year, Semester 3rd semester Subject Code: 3131906 Date: 28-10-2021 Subject Name: Kinematics and Theory of Machine Time: 1:15 Hour Total Marks: 30 Instructions: 1. All questions are compulsory. 2. Figures to the right indicates full marks. 3. Make suitable assumptions wherever necessary. Questionnaires M B.T. CO’s Q:1 (a) Distinguish between: 03 Und. CO1 1. Mechanism & machine 2. Lower & higher pairs 3. Machine & Structure (b) Sketch and describe the working of ONE type of quick return mechanisms. 07 CO1 OR (b) Sketch and explain any ONE inversions of a double slider crank chain. 07 Und. CO1 Q:2 (a) Define 1. Module 2. Pitch 3. Addendum 03 Und. CO2 (b) In a reverted epicyclic gear train, the arm F carries two wheels A and D and a 07 E CO2 compound wheel B, C. The wheel A meshes with wheel B and the wheel D meshes with wheel C. ZA=80, ZD=48 and ZC=72. Find the speed and direction of wheel D when wheel A is fixed and arm F makes 240 rpm clockwise. OR (b) State and prove the “Law of gearing” 07 Und. CO2  Q.3 In Fig. the angular velocity of the 10 Und CO4 crank OA is 600 r.p.m. Determine the An linear velocity of the slider D and the angular velocity of the link BD, when the crank is inclined at an angle of 75° to the vertical. The dimensions of various links are: OA = 28 mm; AB = 44 mm; BC 49 mm; and BD = 46 mm. The center distance between the centers of rotation O and C is 65 mm. The path of travel of the slider is 11 mm below the fixed point C. The slider moves along a horizontal path and OC is vertical. OR Q.3 A cam drives a flat reciprocating follower in the following manner : During 10 E CO4 first 120° rotation of the cam, follower moves outwards through a distance of 20 mm with simple harmonic motion. The follower dwells during next 30° of cam rotation. During next 120° of cam rotation, the follower moves inwards with simple harmonic motion. The follower dwells for the next 90° of cam rotation. The minimum radius of the cam is 25 mm. Draw the profile of the cam. M : Marks, B.T. - Blooms of Taxonomy, Und. – Understand, An: Analyze, A: Apply, E = Evaluate, C = Create, CO: Course Objective Q.3 In Fig. the angular velocity of the 10 Und CO4 crank OA is 600 r.p.m. Determine the An linear velocity of the slider D and the angular velocity of the link BD, when the crank is inclined at an angle of 75° to the vertical. The dimensions of various links are: OA = 28 mm; AB = 44 mm; BC 49 mm; and BD = 46 mm. The center distance between the centers of rotation O and C is 65 mm. The path of travel of the slider is 11 mm below the fixed point C. The slider moves along a horizontal path and OC is vertical. OR Q.3 A cam drives a flat reciprocating follower in the following manner : During 10 E CO4 first 120° rotation of the cam, follower moves outwards through a distance of 20 mm with simple harmonic motion. The follower dwells during next 30° of cam rotation. During next 120° of cam rotation, the follower moves inwards with simple harmonic motion. The follower dwells for the next 90° of cam rotation. The minimum radius of the cam is 25 mm. Draw the profile of the cam. M : Marks, B.T. - Blooms of Taxonomy, Und. – Understand, An: Analyze, A: Apply, E = Evaluate, C = Create, CO: Course Objective  C. K. Pithawala College of Engineering and Technology Mechanical Engineering Department Mid Semester Examination [Winter- 2022] B.E. 2nd Year, Semester 3rd semester Subject Code: 3131906 Date: 20-12-2022 Subject Name: Kinematics and Theory of Machine Time:1:15 Hour Total Marks: 30 Instructions: 1. All questions are compulsory. 2. Figures to the right indicates full marks. 3. Make suitable assumptions wherever necessary. Questionnaires M B.T. CO’s Q:1 (a) Define the following: 03 Und. CO1 1. Degree of Freedom 2. Lower pairs 3. Inversion (b) Sketch and explain any ONE inversions of a four-bar chain. 07 U CO1 OR (b) Sketch and explain any ONE inversions of a double slider crank chain. 07 Und. CO1 Q:2 (a) Derive the empirical relation for the ratio of driving tensions for flat belt drive. 03 Und. CO2 (b) A shaft rotating at 200 r.p.m. drives another shaft at 300 r.p.m. and transmits 6 07 E CO2 kW through a belt. The belt is 100 mm wide and 10 mm thick. The distance between the shafts is 4m. The smaller pulley is 0.5 m in diameter. Calculate the stress in the belt, if it is 1. An open belt drive, 2. A cross belt drive. Take µ=0.3 OR (b) An open belt drive connects two pulleys 1.2 m and 0.5 m diameter, onparallel 07 E CO2 shafts 4 metres apart. The mass of the belt is 0.9 kg per metre length and the maximum tension is not to exceed 2000 N.The coefficient of friction is 0.3. The 1.2 m pulley, which is the driver, runs at 200 r.p.m. Due to belt slip on one of the pulleys, the velocity of the driven shaft is only 450 r.p.m. Calculate the torque on each of the two shafts, the power transmitted Q.3 The mechanism, as shown in Fig., has 10 Und CO4 the dimensions of various links as : An AB = DE = 150 mm; BC = CD = 450 mm; EF = 375 mm. The crank AB makes an angle of 45° with the horizontal and rotates about A in the clockwise direction at a uniform speed of 120 r.p.m. The lever DC oscillates about the fixed point D, which is connected to AB by the coupler BC. The block F moves in the horizontal guides, being driven by the link EF. Determine:1. velocity of the block F, 2. angular velocity of DC, and 3.rubbing speed at the pin C which is 50 mm in diameter. OR Q.3 Draw the cam profile for the following conditions: Follower type=knife edge d 10 E CO4 follower, in line; lift=30mm;base circle radius =20mm;outstroke with uniformvelocity in 120°of cam rotation;dwell for 60°; return stroke with uniform velocity, during 90°of camrotation; dwell for the remaining period. M : Marks, B.T. - Blooms of Taxonomy, Und. – Understand, An: Analyze, A: Apply, E = Evaluate, C = Create, CO: Course Objective  C. K. Pithawala College of Engineering and Technology Mechanical Engineering Department Mid Semester Examination [Winter- 2021] B.E. 2nd Year, Semester 3rd semester Subject Code: 3131906 Date: 09-12-2021 Subject Name: Kinematics and Theory of Machine Time: 1:15 Hour Total Marks: 30 Instructions: 1. All questions are compulsory. 2. 2. Figures to the right indicates full marks. 3. 3. Make suitable assumptions wherever necessary. Questionnaires M B.T. CO’s Q:1 1. The linear velocity of a body rotating at ω rad/s along a circular path of 10 Und CO3 radius r is given by a) ω.r b) ω/r c) ω2.r d) ω2/r 2. The angular velocity (in rad/s) of a body rotating at N r.p.m. is a) π N/60 b) 2 π N/60 c) π N/120 d) π N/180 3. ABCD is a four bar mechanism in which AB = 310mm & CD = 450mm. AB and CD are both perpendicular to the fixed link AD. If the velocity of B at this condition is v. Then the velocity of C is a) v b) 2/3 v c) 3/2 v d) 9/4 v 4. The component of the acceleration, parallel to the velocity of the particle, at the given instant is called a) radial component b) tangential component c) Coriolis component d) none of the mentioned 5. The component of the acceleration, perpendicular to the velocity of the particle, at the given instant is called a) radial component b) tangential component c) Coriolis component d) none of the mentioned 6. A point B on a rigid link AB moves with respect to A with angular velocity ω rad/s. The total acceleration of B with respect to A will be equal to a) vector sum of radial component and Coriolis component b) vector sum of tangential component and Coriolis component c) vector sum of radial component and tangential component d) vector difference of radial component and tangential component 7. The direction of velocity is parallel if the rotation is anticlockwise and perpendicular to the line joining links if the rotation is clockwise. a) True b) False 8. In the above question, if both the links OA and OB turns in clockwise direction, then the rubbing velocity at the pin joint O is a) ω1.ω2.r b) (ω1-ω2)r c) (ω1+ω2)r d) (ω1-ω2)2r 9. The relative velocity of B with respect to A in a rigid link AB is a) parallel to AB b) perpendicular to AB c) along AB d) at 450 10. What is the correct representation of velocity of point A with respect to B in a link? a) Vab b) Vba c) Va-b d) Vb-a  Q.2 In the mechanism shown in Fig., the 10 Und CO4 slider C is moving to the right with a An velocity of 1 m/s and an acceleration of 2.5 m/s2. The dimensions of various links are AB = 3 m inclined at 45° with the vertical and BC = 1.5 m inclined at 45° with the horizontal. Determine: 1. The magnitude of vertical and horizontal component of the acceleration of the point B, and 2. the angular acceleration of the links AB and BC. OR Q.2 (a) Derive an expression for the magnitude and direction of Coriolis component of 04 Und CO4 acceleration. (b) State and prove the Kennedy’s theorem as applicable to instantaneous centres of 03 rotation of three bodies. How is it helpful in locating various instantaneous centres of a mechanism? (c) Explain Angular Velocity Theorem 03 Q.3 (A) Explain Friction and Law of friction. 03 Und. CO5 (B) A shaft rotating at 200 r.p.m. drives another shaft at 300 r.p.m. and transmits 6 07 E CO5 kW through a belt. The belt is 100 mm wide and 10 mm thick. The distance between the shafts is 4m. The smaller pulley is 0.5 m in diameter. Calculate the stress in the belt, if it is 1. An open belt drive, and 2. A cross belt drive. Take µ=0.3 OR (B) Derive Equation of Length of belt for open belt drive 07 Und. CO5 M : Marks, B.T. - Blooms of Taxonomy, Und. – Understand, An: Analyze, A: Apply, E = Evaluate, C = Create, CO: Course Objective  GUJARAT TECHNOLOGICAL UNIVERSITY C.K.PITHAWALA COLLEGE OF ENGINEERING AND TECHNOLOGY, SURAT ASSIGNMENT 1 Subject Name KINEMATICS AND THEORY OF MACHINES Subject Code 3131906 Concept Understand basic structure and elements of machines Student Class 2nd Year (3rd Semester) Mechanical Engineering Academic Year MECHANICAL ENGINEERING DEPARTMENT  ASSIGNMENT 1 Sr Assignment Question No 1 Differentiate giving examples: 1. Lower and higher pairs 2. Mechanism and machine 3. Turning and rolling pairs. 4. Binary Joint and Binary Pair 2 State and explain types of constrained motion 3 Define Grashof’s law. State how is it helpful in classifying the four-link mechanisms into different types? 4 Calculate Degree of freedom for following mechanism: 5 In a crank and slotted lever quick return motion mechanism, the distancebetween the fixed centres is 240 mm and the length of the driving crank is 120 mm. Find the inclinationof the slotted bar with the vertical in the extreme position and the time ratio of cutting stroke tothe return stroke. If the length of the slotted bar is 450 mm, find the length of the stroke if the line of strokepasses through the extreme positions of the free end of the lever. 6 Explain (1) Peaucellier mechanism and (2) Roberts mechanism with neatsketch What are quick return motion mechanisms? Where are they used? Discuss the functioning of any one of them. Answer in short: 1. What is the number of degree of freedom (n) when the mechanism forms a structure? 2. In a kinematic chain, a quaternary joint is equal to how many binary joints? 3. Which type of pair has been made by the lead screw of a lathe with nut? 4. Which mechanism is used to enlarge or reduce the size of drawing? 5. Write down the equation about the relation between numbers of pairs (p) forming the kinematic chain and the number of links (l). Give a neat sketch of the straight line motion “Hart Mechanism”. What are rigid and resistance bodies? Elaborate. What are quick return motion mechanisms? Where are they used? Discuss the functioning of any one of them. GUJARAT TECHNOLOGICAL UNIVERSITY  C.K.PITHAWALA COLLEGE OF ENGINEERING AND TECHNOLOGY, SURAT ASSIGNMENT 2 Subject Name KINEMATICS AND THEORY OF MACHINES Subject Code 3131906 Concept Identify functional characteristics of various machine elements Student Class 2nd Year (3rd Semester) Mechanical Engineering Academic Year MECHANICAL ENGINEERING DEPARTMENT  ASSIGNMENT 2 Sr Assignment Question No 1 Explain the term “Interference” as applied to gears? 2 State any three application of Gear Train. 3 A pair of spur gears with involute teeth is to give a gear ratio of 4:1. The arc of approach is not to be less than the circular pitch and the smaller wheel is driver. The angle of the pressure is 14.50. Find: (1) The least number of teeth that can be used on each wheel, and (2) The addendum of the wheel in terms of the circular pitch? 4 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 r.p.m. in the anticlockwise direction about the center of the gear A which is fixed, Determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction what will be the speed if gear B? 5 A cam with 30 mm as minimum diameter is rotating clockwise as a uniform speed of 1200 rpm and has to give the motion to the roller follower 10 mm diameter as defined below: (1) Outward stroke of 25 mm during 1200 of cam rotation with equal uniform acceleration and retardation (2) Dwell for 600 cam rotation (3) Return to its initial position during 900 of cam rotation with equal uniform acceleration and retardation (4) Dwell for the remaining 900 cam rotation. Layout the cam profile when the roller axis is offset to right by 5 mm. 6 A cam is to be designed for a knife edge follower with the following data: (1) Cam lift=40 mm during 900 of cam rotation with SHM (2) Dwell for the next 300 (3) During the next 600 of the cam rotation, the follower returns to its original position with uniform velocity. (4) Dwell during the remaining 1800  GUJARAT TECHNOLOGICAL UNIVERSITY C.K.PITHAWALA COLLEGE OF ENGINEERING AND TECHNOLOGY, SURAT ASSIGNMENT 3 Subject Name KINEMATICS AND THEORY OF MACHINES Subject Code 3131906 Concept Synthesize various mechanisms based on position, velocity and acceleration requirement Student Class 2nd Year (3rd Semester) Mechanical Engineering Academic Year MECHANICAL ENGINEERING DEPARTMENT  ASSIGNMENT 3 Sr Assignment Question No 1 Define the following term related to synthesis: a. Type synthesis b. Number synthesis c. Dimensional synthesis d. Function generation e. Path generation f. Body guidance 2 Explain Freudenstein’s equation. 3 Four bar crank–rocker quick return linkage for specified time ratio = 1:1.25 with 450 output rocker motion. Design the synthesis. 4 Design a four bar link mechanism if the motions of the input and output links are governed by a function. Assume to vary from 300 to 1200 and from 600 to 1300. The length of the fixed link is 30 mm. Use Chebychev spacing of accuracy points. 5 Synthesis a function generator to solve the equation = over the range 1 ≤ x ≤ 2 using three precision positions. 6 Using Bloch method , synthesis and also draw a four bar linkages to meet the following specifications of angular position, velocities and accelerations at one of its positions are = 21 / , = −280 / = −6 / , = 200 / = 12 / , = 100 / Design a four bar link mechanism if the motions of the input and output links aregoverned by a function y= x1.51 ≤ x ≤ 4. AssumeƟ to vary from 300 to 1200and Øfrom 600 to 1300. The length of the fixed link is 30 mm. Use Chebychevspacing of accuracy points. Design a four bar mechanism with input link „a‟, coupler link ‟b‟ and output link „c‟. angles θ and Φ for threesuccessive position are given in table below: 1 2 3 0 0 Ɵ 20 35 500 0 0 Ø 35 45 600 Using Freudenstein’s Equation find out other link lengths b, c and d. assume link length a = 1. Synthesize a four bar chain mechanism by using Freudenstein’s Equation for thefollowing positions of input-fixed link “a” Synthesize the mechanism for following three successive position with length of fixed link =50mm. Ɵ1 = 180⁰ Ø1 =90⁰, Ɵ2 = 135⁰ Ø2 = 80⁰, Ɵ3 = 90⁰ Ø3 = 60⁰ Explain the Freudenstein’s Equation for four bar chain mechanism.  GUJARAT TECHNOLOGICAL UNIVERSITY C.K.PITHAWALA COLLEGE OF ENGINEERING AND TECHNOLOGY, SURAT ASSIGNMENT 4 Subject Name KINEMATICS AND THEORY OF MACHINES Subject Code 3131906 Concept Determine position, velocity and acceleration of linkages in mechanism at any instant Student Class 2nd Year (3rd Semester) Mechanical Engineering Academic Year MECHANICAL ENGINEERING DEPARTMENT  ASSIGNMENT 4 Sr Assignment Question No 1 A crank and rocker mechanism ABCD has the following dimensions. AB = 0.75m, BC = 1.25m, CD = 1m, AD = 1.5m, E is the midpoint of the coupler link BC. AD is the fixed link. Crank AB has a angular velocity of 20 rad/s counter clockwise and deceleration of 280 rad/s2 at the instant angle DAB = 600 find 1. Instantaneous linear velocity and acceleration of midpoint E of link BC. 2. Instantaneous angular velocity and acceleration of link CD. 2 Explain Angular Velocity Theorem 3 Using relative velocity method to find the absolute velocity of the slider E in the mechanism as shown in fig., when the crank rotates at 60 rpm. O1A=5cm,O2B=12cm,AB=27cm,O2D=9cm, DE= 18cm 4 State and prove the Kennedy’s theorem as applicable to instantaneous centres of rotation of three bodies. How is it helpful in locating various instantaneous centres of a mechanism? 5 The crank of a slider crank mechanism rotates clockwise at a constant speed of 300 rpm. The crank is 150 mm and connecting rod is 600 mm long. Determine1. Linear velocity and acceleration of midpoint of connecting rod2. Angular velocity and angular acceleration of the connecting rod, at a crank angle of 450 from inner dead centre position. 6 Derive an expression for the magnitude and direction of Coriolis component ofacceleration.  GUJARAT TECHNOLOGICAL UNIVERSITY C.K.PITHAWALA COLLEGE OF ENGINEERING AND TECHNOLOGY, SURAT ASSIGNMENT 5 Subject Name KINEMATICS AND THEORY OF MACHINES Subject Code 3131906 Concept Understand basics related to friction and its practical application in mechanical engineering Student Class 2nd Year (3rd Semester) Mechanical Engineering Academic Year MECHANICAL ENGINEERING DEPARTMENT  ASSIGNMENT 5 Sr Assignment Question No 1 In a flat belt drive, the initial tension measured in International System of units is 2500. The coefficient of friction between the belt and the pulley is 0.35 and the angle of lap on the smaller and larger pulleys are 160° and 180° respectively. Determine the Horse Power transmitted by belt if smaller pulley of 200 mm diameter rotates at 420 revolutions per minute. 2 Two mating involute spur gear of 20 degree pressure angle have a gear ratio of 2. The number of teeth on the pinion is 20 and its speed is 250 rpm. Module pitch of the teeth is 12 mm. Find: (1) The addendum for pinion (2) The addendum for gear wheel & (3) The length of the arc of contact. Assume pinion to be the driver 3 What are different types of chains? Explain with neat sketches, the power transmission chains. 4 Derive the equation of effort required to move the body up the plane considering friction 5 Derive the expression for the frictional torque of a flat pivot bearing assuming (i) Uniform pressure theory (ii) Uniform wear theory. 6 A multiple disc clutch transmits 75 kW of power at 2000 rpm. Coefficient of friction for the friction surfaces is 0.2. Axial intensity of pressure is not to exceed 180 kN/m2. Internal radius is 100 mm and is 0.8 times the external radius. Find the number of plates needed to transmit the required torque.Assume uniform wear conditions.  Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER– III EXAMINATION – SUMMER 2020 Subject Code: 3131906 Date:04/11/2020 Subject Name: Kinematics and Theory of Machine Time: 02:30 PM TO 05:00 PM Total Marks: 70 Instructions: 1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. MARKS Q.1 (a) Define the following terms: 03 (1) Module of gear (2) Pressure angle in cam-profile (3) Self-locking brake. (b) Define the following terms 04 (1) Lower pair (2) Higher pair (3) successfully constrained motion (4) completely constrained motion (c) Explain the working principle of any quick return mechanism with net sketch. 07 Q.2 (a) Explain the relation between linear and angular terms: displacement, velocity 03 and acceleration (b) In a crank and slotted lever quick return mechanism, the distance between the 04 fixed centers is 300 mm and the length of the driving crank is 150 mm. Determine the ratio of the time taken on the cutting and return strokes (c) The crank of a slider crank mechanism rotates clockwise at a constant speed 07 of 10 rad/s. The crank OA is 150 mm and connecting rod AB is 600 mm long. Determine the acceleration of connecting rod AB, acceleration of slider B. When crank is at 45o from inner dead center position. OR (c) A four-bar mechanism ABCD, the length of the various links is given as AB 07 =190 mm, BC = CD =280 mm, AD = 500 mm. ∠BAD = 550. The crank rotates at 10 rad/s in the clock wise direction. Determine... (a) the acceleration of link BC and CD and (b) the angular acceleration of link BC and CD. Q.3 (a) Explain Rigid link, Flexible link and Fluid link with example. 03 (b) State and prove ‘Aronhold Kennedy’s Theorem’ of three instantaneous 04 centers. (c) Synthesize a four-bar mechanism to meet the following instantaneous 07 conditions for input output links: θ2 = 600, θ4 = 900 ω2 = 3 rad/sec, ω4 = 2 rad/sec α2 = -1 rad/sec2, α4 = 0 1  OR Q.3 (a) Define rubbing velocity at a pin joint. What will be the rubbing velocity at 03 pin joint when the two links move in the same and opposite directions? (b) Explain in brief Function, Path & Motion Generation 04 (c) Design a four-bar chain mechanism, governed by the function y= 2x2 for the 07 range 2 ≤ x ≤ 4 Assuming θ vary between 400 and 1200 for the input link and ϕ vary between 600 and 1320 for the output link. Find the value of x , y , ϕ and φ corresponding to three precision point. Q.4 (a) What do you understand by the term “interference” as applied to the gear? 03 (b) Bridges and roof of workshop uses structure element, justify with reason. 04 (c) Draw the cam profile operating knife edge follower from following data 07 (i) Follower to move out through distance of 40mm during 100° (ii) Follower to dwell for next 80°. (iii) Follower to return to its initial position during 90°. (iv) Follower to dwell for remaining cam rotation The cam shaft rotates at 900rpm. The minimum radius of cam is 50mm and line of follower is offset 15mm from the axis of the cam and displacement to take place with uniform acceleration and retardation for both inward and outward stroke. OR Q.4 (a) Define the following terms: (1) Dry friction (2) Film friction (3) Limiting 03 angle of friction (b) Find maximum velocity and acceleration for outward and return stroke for 04 the data given in above problem 4(c) and draw the displacement, velocity and acceleration diagram. (c) Explain with sketches the different types of cams and followers 07 Q.5 (a) Show that velocity ratio for compound belt drive is given by 03 (b) Derive an expression for the length of path of contact for two involutes 04 profile gear in mash. (c) The pressure angle of two gear in mesh is 200 and have a module of 10mm. 07 The number of teeth on pinion are 24 and on gear 60. The addendum of pinion and gear is same and equals to one module. Determine... (a) the number of pairs of teeth in contact (b) the angle of action of the pinion and gear. OR Q.5 (a) Explain the phenomena of slip and creep in a belt drive. 03 (b) Explain with the neat sketch the “sun and planet wheel”. 04 (c) Find the power transmitted by a belt running over a pulley of 600mm 07 diameter at a speed of 200 rpm. The coefficient of friction between belt and the pulley is 0.25, angle of lap 160° and maximum tension in the belt is 2500 N. 2 Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER– III (NEW) EXAMINATION – SUMMER 2022 Subject Code:3131906 Date:18-07-2022 Subject Name:Kinematics and Theory of Machines Time:02:30 PM TO 05:00 PM Total Marks:70 Instructions: 1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. 4. Simple and non-programmable scientific calculators are allowed. MARKS Q.1 (a) Sketch and describe four bar chain mechanism. 03 (b) Explain the terms: 1. Lower pair 2. Higher pair 3. Kinematic link 04 4. Mechanism (c) Compare and discuss: kinematic link, kinematic pair, and 07 kinematic chain. Q.2 (a) Create displacement diagram for Simple Harmonic motion for 03 desired dimensions. (b) Draw the displacement, velocity and acceleration diagrams for a 04 follower when it moves with Uniform acceleration and retardation (c) A cam is to be designed for a knife edge follower with the 07 following data : 1. Cam lift = 40 mm during 90° of cam rotation with simple harmonic motion. 2. Dwell for the next 30°. 3. During the next 60° of cam rotation, the follower returns to its original position with simple harmonic motion. 4. Dwell during the remaining 180°. Draw the profile of the cam when the line of stroke is offset 20 mm from the axis of the cam shaft. The radius of the base circle of the cam is 40 mm. Determine the maximum velocity and acceleration of the follower during its ascent and descent, if the cam rotates at 240 r.p.m OR (c) Draw the profile of the cam when the roller follower moves with 07 cycloidal motion during out stroke and return stroke, as given below : 1. Out stroke with maximum displacement of 31.4 mm during 180° of cam rotation, 2. Return stroke for the next 150° of cam rotation, 3. Dwell for the remaining 30° of cam rotation. The minimum radius of the cam is 15 mm and the roller diameter of the follower is 10 mm. The axis of the roller follower is offset by 10 mm towards right from the axis of cam shaft. Q.3 (a) Explain the terms: Function Generation, Path Generation, Motion 03 Generation (b) Formulate freudenstein’s equation. 04 (c) Locate all the instantaneous centres of the slider crank mechanism 07 as shown in Fig. The lengths of crank OB and connecting rod AB 1  are 100 mm and 400 mm respectively. If the crank rotates clockwise with an angular velocity of 10 rad/s, find: 1. Velocity of the slider A, and 2. Angular velocity of the connecting rod AB OR Q.3 (a) State and prove ‘Aronhold Kennedy’s Theorem’ of three 03 instantaneous centres. (b) Explain briefly dimensional synthesis. 04 (c) A four bar chain mechanism is to be designed, by using three 07 precision point to generate the function Y = X1.5 for the range 1 ≤ x ≤ 4 Assuming 300 starting position and 1200 finishing position for the input link and 900 starting position and 1800 finishing position for the output link, find the value of x , y , ɵ and φ corresponding to three precision point. Q.4 (a) Differentiate between Involute and Cycloidal profile of gear tooth 03 (b) Define the term: 04 1. Pitch circle 2. Pitch Diameter 3. Pitch Point 4. Module (c) In an epicyclic gear train, an arm carries two gears A and B having 07 36 and 45 teeth respectively. If the arm rotates at 150 r.p.m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B? OR Q.4 (a) Define the following terms: 03 (1) Dry friction (2) Film friction (3) Limiting angle of friction (b) Discuss the various types of the brakes 04 (c) A bicycle and rider of mass 100 kg are travelling at the rate of 16 07 km/h on a level road. A brake is applied to the rear wheel which is 0.9 m in diameter and this is the only resistance acting. How far will the bicycle travel and how many turns will it make before it comes to rest? The pressure applied on the brake is 100 N and µ = 0.05. Q.5 (a) Explain what do you understand by ‘initial tension in a belt’ 03 (b) Interpret the Phenomenon of “slip”& “creep” in a belt drive. 04 (c) Power is transmitted using a V-belt drive. The included angle of 07 V-groove is 30°. The belt is 20 mm deep and maximum width is 20 mm. If the mass of the belt is 0.35 kg per metre length and 2  maximum allowable stress is 1.4 MPa, determine the maximum power transmitted when the angle of lap is 140°. µ = 0.15. OR Q.5 (a) Show cone clutch with sketch. 03 (b) Illustrate with the neat sketch the “sun and planet wheel.” 04 (c) Explain the condition for correct steering. Sketch and show the 07 Davis steering mechanism and discuss their advantages. ************* 3 Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III(NEW) EXAMINATION – SUMMER 2023 Subject Code:3131906 Date:01-08-2023 Subject Name:Kinematics and Theory of Machines Time:02:30 PM TO 05:00 PM Total Marks:70 Instructions: 1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. 4. Simple and non-programmable scientific calculators are allowed. Q.1 (a) Define the following terms. 03 Link, Higher Pair, Mechanism, Machine (b) Write a inversion of double slider crank and explain any one inversion of 04 double slider crank. (c) What is degree of freedom in mechanism ? explain grublers crieteria. 07 Q.2 (a) Explain terms: relative velocity, corroilis component in acceleration, 03 peripheral velocity (b) What is instantaneous center? Explain kennedys theorm. 04 (c) Derive the equation of displacement, velocity and acc crank by slider 07 craeleration of slider in slider crank mechanism. OR (c) Following data relates to reciprocating steam engine having crank 14.5 07 cm, connecting rod 60 cm, uniform speed of crank 250 rpm, radius of pin circle 15 cm, length of connecting rod between centers 60 cm. Direction of rotation of crank is clockwise when crank has turned 30 degree from inner dead center. Find acceleration of piston, acceleration of center of gravity of connecting rod. The center of gravity being 22 cm from big end center(piston end connection). Q.3 (a) Explain analytic synthesis for four bar mechanism. 03 (b) Explain limiting tension rato in flat belt drive and derive its equation. 04 (c) State chebishev spacing for mechanism and find three precision points for 07 the function f(x) = x1.3 in the interval 0≤x ≤ 6 , take θc = 60°, Φ1 = 50° and ΔΦ = 100° OR Q.3 (a) What is synthesis? Explain type of synthesis. 03 (b) Explain three position synthesis for four bar mechanism. 04 (c) How many V Belts required to transmit 30 kw from grooved pulley of 07 250 mm pitch diameter with groove angle 34° rotating at 1000 rpm to another grooved pulley of 1m pitch diameter. Maximum load per belt is 700 N, mass of 1 belt is 0.3 kg, coefficient of friction is 0.2 center distance is 1meter. Q.4 (a) Explain various application of cam. 03 (b) Describe with neat sketch working of single friction clutch. 04 1  (c) Draw the cam profile for roller follower of 30 mm diameter having lift of 07 follower ( ascend) 50 mm during 90° of cam rotation with SHM, follower having 30° of dwell period, the follower with decent to its original position during 90° of cam rotation with uniform acceleration and deacceleration it remains rest for rest of the cam operation. Least radius of cam 50 mm, if it rotates 300 rpm find maximum velocity and acceleration during ascent and decent. OR Q.4 (a) Write a short note on internal expanding shoe brake. 03 (b) State the type of motion for follower. Explain any one type of motion 04 with neat sketch. (c) A conical pivot supports a load of 25 KN. The intensity of pressure is 0.5 07 MN/mm2. Find the diameter of bearing surface and its cone angle if the face width is 0.75 times its diameter. If friction coefficient is 0.06 and shaft runs at 120 rpm find the power lost in friction. Q.5 (a) What is interference in gears ? How it can be avoided ? 03 (b) Write a short note on automobile differential gear box. 04 (c) Determine minimum number of teeth required on pinion & wheel to 07 avoid interference when gear ratio is 3 & when number of teeth on pinion and wheel is equal, consider pressure angle 20° and assume addendum of gear is 1.1 module. OR Q.5 (a) Write a short note on Epicyclic Gear Train 03 (b) Derive the expression for velocity of sliding of the mating teeth. 04 (c) An Epicyclic gear train of a sun and planet type has the fixed outer 07 annular A. Sun wheel S rotating at a speed of 800 revolutions/minute. In clockwise direction and arm E carrying three planet wheels P needed to be driven. If the diameteral pitch is same for all mating gears and sun wheel S and planet wheel P have 15 and 45 teeth respectively. Determine number of teeth on annular A and speed of direction of rotation of planet. ************* 2 Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER– III (New) EXAMINATION – WINTER 2019 Subject Code: 3131906 Date: 3/12/2019 Subject Name: Kinematics and Theory of Machine Time: 02:30 PM TO 05:00 PM Total Marks: 70 Instructions: 1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. Marks Q.1 (a) Define the following terms. 03 1. Higher pair 2. Completely Constrained motion 3. Structure (b) Apply Kutzbach’s criterion to find degree of freedom of the 04 following mechanisms and also predict the motion. (c) Enlist the quick return mechanisms and describe working of 07 any one of them with neat sketch. Q.2 (a) Explain types of Instantaneous centers of mechanism. 03 (b) Prove that if three links move relatively to each other they 04 have three instantaneous centers which must lie on a straight line. (c) Following data related to reciprocating steam engine as 07 shown in fig. When the crank has turned 30° from inner dead centre. Find: (i) Acceleration of piston (ii) Acceleration of C point on connecting rod. OR (c) In the toggle mechanism, as shown in Fig., the slider D is 07 constrained to move on a horizontal path. The crank OA is rotating in the counter-clockwise direction at a speed of 180 r.p.m. The dimensions of various links are as follows : OA = 180 mm ; CB = 240 mm ; AB = 360 mm ; and BD = 540 mm. For the given configuration, find : 1. Velocity of slider D, 2. Angular velocity of links AB, CB and BD 1 Q.3 (a) Explain the phenomena of slip and creep in a belt drive. 03 (b) Construct two position synthesis of single slider crank 04 mechanism by relative pole method. (c) A four bar mechanism is to be designed, by using three 07 precision points, to generate the function y = x1.5 , for the range 1 ≤ x ≤ 4. Assuming 30° starting position and 120° finishing position for the input link and 90° starting position and 180° finishing position for the output link, find the values of x, y, θ and φ corresponding to the three precision points. OR Q.3 (a) List and describe the three phases of synthesis. 03 (b) Derive the empirical relation for the ratio of driving tensions 04 for flat belt drive. (c) A shaft rotating at 200 r.p.m. drives another shaft at 300 07 r.p.m. and transmits 6 kW through a belt. The belt is 100 mm wide and 10 mm thick. The distance between the shafts is 4m. The smaller pulley is 0.5 m in diameter. Calculate the stress in the belt, if it is an open belt drive, Take μ = 0.3. Q.4 (a) Define the following terms: 03 (1) Dry friction (2) Film friction (3) Limiting angle of friction (b) A vehicle moving on a rough plane inclined at 10° with the 04 horizontal at a speed of 36 km/h has a wheel base 1.8 metres. The centre of gravity of the vehicle is 0.8 metre from the rear wheels and 0.9 metre above the inclined plane. Find the distance travelled by the vehicle before coming to rest and the time taken to do so when The vehicle moves up the plane. The brakes are applied to all the four wheels and the coefficient of friction is 0.5. (c) Construct a cam, with a minimum radius of 30 mm, rotating 07 clockwise at a uniform speed is to be designed to give a roller follower, at the end of a valve rod, motion described below : 1. To raise the valve through 50 mm during 120° rotation of the cam ; 2. To keep the valve fully raised through next 30°; 3. To lower the valve during next 60°; and 4. To keep the valve closed during rest of the revolution i.e. 150° ; The diameter of the roller is 20 mm and the diameter of the cam shaft is 25 mm. Draw the profile of the cam when the line of stroke of the valve rod passes through the axis of the cam shaft, The displacement of the valve, while being raised and lowered, is to take place with simple harmonic motion. OR 2 Q.4 (a) Explain with reason the case in which the shoe of the single 03 shoe brake will be pivoted. (b) The inner and outer radii of a single plate clutch are 40 mm 04 and 80 mm respectively. Determine the maximum, minimum and the average pressure when the axial force is 3 kN. (c) Construct a cam, with a minimum radius of 50 mm, rotating 07 clockwise at a uniform speed, is required to give a knife edge follower the motion as described below : 1. To move outwards through 40 mm during 100° rotation of the cam ; 2. To dwell for next 80° ; 3. To return to its starting position during next 90°, and 4. To dwell for the rest period of a revolution i.e. 90°. Draw the profile of the cam when the line of stroke of the follower is off-set by 15 mm. The displacement of the follower is to take place with uniform acceleration and uniform retardation. Q.5 (a) Draw a neat sketch of single plate clutch and also label each 03 component. (b) State and derive the law of gearing. 04 (c) Two 20° involute spur gears have a module of 10 mm. The 07 addendum is one module. The larger gear has 50 teeth and the pinion has 13 teeth. Does interference occur? If it occurs, to what value should the pressure angle be changed to eliminate interference? OR Q.5 (a) Define the following terms: 03 (1) Module of gear (2) Backlash (3) Self locking brake (b) Make a comparison of cycloidal and involute tooth form. 04 (c) An epicyclic gear consists of three gears A, B and C as shown 07 in Fig. The gear A has 72 internal teeth and gear C has 32 external teeth. The gear B meshes with both A and C and is carried on an arm EF which rotates about the centre of A at 18 r.p.m.. If the gear A is fixed, determine the speed of gears B and C. ************** 3 Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE- SEMESTER–III (NEW) EXAMINATION – WINTER 2020 Subject Code:3131906 Date:05/03/2021 Subject Name:Kinematics and Theory of Machine Time:10:30 AM TO 12:30 PM Total Marks:56 Instructions: 1. Attempt any FOUR questions out of EIGHT questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. Marks Q.1 (a) What are usual types of joints in a mechanism? 03 (b) Define: Kinematic link, Kinematic chain, Mechanism, Lower pair. 04 (c) Illustrate the inversion of a double slider crank mechanism giving example. 07 Q.2 (a) Contrast Linear velocity & Velocity of rubbing. 03 (b) Interpret the Phenomenon of “slip”& “creep” in a belt drive. 04 (c) Derive the relation for ratio of belt tension in a flat belt drive. 07 Q.3 (a) State and explain angular-velocity ratio theorem as applicable to mechanism. 03 (b) Explain briefly dimensional synthesis. 04 (c) An epicyclic train of gears is arranged as shown in Figure. How many 07 revolutions does the arm, to which the pinions B and C are attached, make : 1. when A makes one revolution clockwise and D makes half a revolution anticlockwise, and 2. When A makes one revolution clockwise and D is stationary? The number of teeth on the gears A and D are 40 and 90 respectively. Q.4 (a) Explain solid friction, rolling friction and greasy friction. 03 (b) What are different types of pulleys? Explain briefly with sketch. 04 (c) The speed ratio of the reverted gear train, as shown in Figure, is to be 12. 07 The module pitch of gears A and B is 3.125 mm and of gears C and D is 2.5 mm. Calculate the suitable numbers of teeth for the gears. No gear is to have less than 24 teeth. 1 Q.5 (a) What is contact ratio? Explain its significance 03 (b) Formulate freudenstein’s equation. 04 (c) Two pulleys, one 450 mm diameter and the other 200 mm diameter are on 07 parallel shafts 1.95 m apart and are connected by a crossed belt. Find the length of the belt required and the angle of contact between the belt and each pulley. What power can be transmitted by the belt when the larger pulley rotates at 200 rev/min, if the maximum permissible tension in the belt is 1 kN, and the coefficient of friction between the belt and pulley is 0.25 ? Q.6 (a) Explain in brief Function, Path & Motion Generation. 03 (b) Differentiate between Involute and Cycloidal profile of gear tooth. 04 (c) State & prove the law of gearing. 07 Q.7 (a) Explain types of constrain motion. 03 (b) Explain internal expanding shoe brake. 04 (c) The crank of a slider crank mechanism rotates clockwise at a constant speed 07 of 300 r.p.m. The crank is 150 mm and the connecting rod is 600 mm long. Determine : 1. Linear velocity and acceleration of the midpoint of the connecting rod, and 2. angular velocity and angular Acceleration of the connecting rod, at a crank angle of 45° from inner dead centre position. Q.8 (a) Explain cone clutch with sketch. 03 (b) Classify followers & explain with neat sketch. 04 (c) A cam is to be designed for a knife edge follower with the following data : 07 1. Cam lift = 40 mm during 90° of cam rotation with simple harmonic motion. 2. Dwell for the next 30°. 3. During the next 60° of cam rotation, the follower returns to its original position with simple harmonic motion. 4. Dwell during the remaining 180°. Draw the profile of the cam when the line of stroke of the follower passes through the axis of the cam shaft. The radius of the base circle of the cam is 40 mm. ************************** 2  Seat No.: ________ Enrolment No.___________ GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III (NEW) EXAMINATION – WINTER 2021 Subject Code:3131906 Date:23-02-2022 Subject Name:Kinematics and Theory of Machines Time:10:30 AM TO 01:00 PM Total Marks:70 Instructions: 1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. 4. Simple and non-programmable scientific calculators are allowed. MARKS Q.1 (a) Define the following term: 03 a) Kinematic chain b) Degree of freedom c) Mechanism (b) Explain different types of kinematic pairs. 04 (c) Explain various inversion of double slider kinematic chain with examples. 07 Q.2 (a) Describe working principle of internal expanding shoe brake with a neat sketch. 03 (b) Construct three position synthesis of single slider crank mechanism by relative 04 pole method. (c) A four bar mechanism is to be designed, by using three precision points, to 07 generate the function y = x 1.5 , for the range 1 ≤ x ≤ 4. Assuming 30° starting position and 120° finishing position for the input link and 90° starting position and 180° finishing position for the output link, find the values of x, y, θ and φ corresponding to the three precision points. OR (c) Derive Freudenstein's equation for four bar mechanism. 07 Q.3 (a) Explain and prove Arnold Kennedy theorem. 03 (b) Define the terms: 04 a) Instantaneous center b) Body centrode & Space centrode c) Relative velocity (c) In a four bar chain ABCD, AD is fixed and is 150 mm long. The crank AB is 40 07 mm long and rotates at 120 r.p.m. clockwise, while the link CD = 80 mm oscillates about D. BC and AD are of equal length. Find the angular velocity of link CD when angle BAD = 60º. OR Q.3 (a) Explain coriolis component and derive its equation. 03 (b) Draw an acceleration diagram of single slider crank mechanism. 04 1  (c) An engine mechanism is shown in fig. The crank CB=100mm and the connecting 07 rod BA=300 mm with G point 100 mm from B. In the position shown, the crank shaft has a speed of 75 rad/sec and an angular acceleration of 1200 rad/sec2. Find 1. velocity of G and angular velocity of AB and 2. acceleration of G and angular acceleration of AB. Q.4 (a) Classify the toothed gear. 03 (b) State and derive law of gearing. 04 (c) Design a cam for operating the exhaust valve of an oil engine. It is required to 07 give equal uniform acceleration and retardation during opening and closing of the valve each of which corresponds to 60º of cam rotation. The valve must remain in the fully open position for 20º of cam rotation. The lift of the valve is 37.5mm and the least radius of the cam is 40mm. The follower is provided with a roller of radius 20mm and its line of stroke passes through the axis of cam. OR Q.4 (a) Define the terms: 03 a) pressure angle b) helix angle c) circular pitch (b) Explain the term 'Interference' as applied to gears. 04 (c) A cam rotating CW at a uniform speed of 1000 rpm is required to give a roller 07 follower the motion defined below: 1. Follower move outwards through 50 mm during 120º of cam rotation 2. Follower to dwell for next 60º of cam rotation 3. Follower to return to its starting position during next 90º of cam rotation 4. Follower to dwell for the rest of the cam rotation. The minimum radius of the cam is 50 mm and diameter of roller is 10mm. The line of stroke of the follower is off set by 20mm from the axis of the cam shaft. If the displacement of the follower takes place with uniform and equal acceleration and retardation on both the outward and return strokes, draw the profile of cam. Q.5 (a) Derive the empirical relation for the ratio of driving tensions for flat belt drive. 03 (b) A casting weighing 9 kN hangs freely from a rope which makes 2.5 turns round a 04 drum of 300 mm diameter revolving at 20 r.p.m. the other end of the rope is pulled by a man. The coefficient of friction is 0.25. Determine: (1) The force required by the man and (2) the power to raise the casting. (c) A multi disc clutch has three discs on the driving shaft and two on the driven shaft. 07 The outside diameter of the contact surfaces is 240mm and inside diameter 120mm. Assuming uniform wear and coefficient of friction as 0.3, find the maximum axial intensity of pressure between the discs for transmitting 25 KW at 1575 rpm. OR Q.5 (a) Define the terms: 03 a) Dry friction b) film friction c) limiting angle of friction (b) Describe with a neat sketch the working of a single plate clutch. 04 (c) A shaft rotating at 200 r.p.m. drives another shaft at 300 r.p.m. and transmits 6 07 kW through a belt. The belt is 100 mm wide and 10 mm thick. The distance between the shafts is 4 m. the smaller pulley is 0.5 m in diameter. Calculate the stress in the belt, if it is (1) an open belt drive, and (2) a cross belt drive. Take µ = 0.3. ************* 2