R5310304-kinematics Of Machinery

1

Code No: R5310304

III B.Tech I Semester(R05) Supplementary Examinations, May 2009 KINEMATICS OF MACHINERY (Mechanical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Define kinematic pair. Distinguish between closed and unclosed type kinematic pairs. Give examples for each type (b) Explain completely, successfully and incompletely constrained motions of kinematics pairs with examples. [7+9] 2. (a) Name the mechanisms that generate straight lines. (b) Prove that the peaucellier mechanism generates a straight-line motion.

[4+12]

3. A crank and rocker mechanism ABCD has the following dimensions: AB =0.75m, BC =1.25 m, CD =1 m, AD =1.5 m and CF = 500 mm. AD is the fixed link. F lies on BC produced. Crank AB has an angular velocity of 30 rad/s counter clock-wise and a deceleration of 200 rad/s2 at the instant angle DAB= 300 . Find (a) The instantaneous linear acceleration of C and F and (b) The instantaneous angular velocities and accelerations of links BC and CD. [16] 4. (a) Sketch polar velocity diagram of a Hooke’s joint and mark its salient features. (b) The angle between the axes of two shafts joined by Hooke’s joint is 20o . The driving shaft rotates at a uniform speed of 200 rpm. The driven shaft carries a steady load corresponding to a power of 7.5 kW. Calculate the mass of the flywheel of the driven shaft if its radius of gyration is 160 mm and the output torque of the driven shaft does not vary by more than 12% of the input shaft. [6+10] 5. (a) Explain the construction of cam profile for simple harmonic motion to the roller follower of the cam. (b) The following data relate to a cam profile in which the follower moves with uniform acceleration and deceleration during ascent and descent. Minimum radius of cam = 25mm, Roller diameter = 7.5mm, Lift = 28mm, Offset of follower axis = 12mm towards right, Angle of ascent = 600 , Angle of descent = 900 , Angle of dwell between ascent and descent = 450 , Speed of the cam = 200 rpm. Draw the profile of the cam and determine the maximum velocity and the uniform acceleration of the follower during the outstroke and the return stroke. [16] 6. (a) Explain the terms, addendum and dedendum. What is clearance? (b) A pinion of 32 involute teeth and 4mm module drives a rack. The pressure angle is 200 . The addendum of both pinion and rack is the same. Determine the maximum permissible value of the addendum to avoid interference. Also, find the number of pairs of teeth in contact. [16] 7. An open belt 100mm wide connects two pulleys mounted on parallel shafts with their centers 2.5m apart. The pulleys are of 500mm and 250mm diameters. The coefficient of friction between the belt and the pulleys is 0.3. the maximum tension in the belt is limited to 15 N/mm width. Find the maximum power which can be transmitted if the larger pulley rotates at 120rpm. [16] 8. (a) Explain about automotive differential. (b) An epicyclic gear consists of a pinion, a wheel of 40 teeth and an annulus with 84 internal teeth concentric with the wheel. The pinion gear with the wheel and the annulus. The arm that carries the axis of the pinion rotates at 100rpm. If the annulus is fixed, find the speed of the wheel; if wheel is fixed, find the speed of the annulus. [16] ?????

2

Code No: R5310304

III B.Tech I Semester(R05) Supplementary Examinations, May 2009 KINEMATICS OF MACHINERY (Mechanical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) What is a Kinematic pair? Explain different types of Kinematic pairs as classified by relative motion. (b) The distance between the axes of two parallel shafts is 1cm. The shafts are connected by Oldham coupling. Find the maximum Kinetic energy of the intermediate piece of mass 5 kg when the shafts revolve at 300rpm. [10+6] 2. (a) Explain watt mechanism and prove that it generates a straight-line motion. (b) Why Watt mechanism is so commonly used to generate an approximate straight-line motion? [12+4] 3. A crank and rocker mechanism ABCD has the following dimensions: AB =0.75m, BC =1.25 m, CD =1 m, AD =1.5 m and CF = 500 mm. AD is the fixed link. F lies on BC produced. Crank AB has an angular velocity of 30 rad/s counter clock-wise and a deceleration of 200 rad/s2 at the instant angle DAB= 300 . Find (a) The instantaneous linear acceleration of C and F and (b) The instantaneous angular velocities and accelerations of links BC and CD. [16] 4. The distance between the pivots of the front stub axles of a car is 130 cm, the length of track rod is 120 cm, the wheel track is 145 cm and the wheelbase is 280cm. What should be the length of track arm if the Ackermann steering gear is to be given a correct steering, when rounding a corner of 6-meter radius? [16] 5. (a) Compare knife edge, roller and mushroom followers. (b) A tangent cam with straight working faces tangential to a base circle of 120mm diameter has a roller follower of 48mm diameter. The line of stroke of the roller follower passes through the axis of the cam. The nose circle radius of the cam is 12mm and the angle between the tangential faces of the cam is 900 . If the speed of the cam is 180rpm, determine the acceleration of the follower when i. During the lift, the roller just leaves the straight flank. [16] ii. The roller is at the outer end of its lift, i.e. at the top of the nose. 6. (a) Explain Bevel gear, worm gears and helical gears. (b) A pair of 200 pressure angle gears in mesh have the following data: Speed of pinion = 400rpm Number of teeth on pinion = 24 Number of teeth on gear = 28 Determine the addendum of the gears if the path of approach and recess is half the maximum value. Determine also the arc of contact and the maximum velocity of sliding between the mating surfaces. [16] 7. A countershaft is to be driven at 240rpm from a driving shaft rotating at 100rpm by an openbelt drive. The diameter of the driving pulley is 480mm. The distance between the centre line of shafts is 2m. Find the width of the belt to transmit 3kW of power if the safe permissible stress in tension is 15N/mm width of the belt. Take µ = 0.3. [16] 8. Determine a suitable train of wheels to satisfy the requirements of a clock, the minute hand of which is fixed to a spindle and the hour hand to a sleeve rotating freely on the same spindle. The pitch is the same for all the wheels and each wheel has at least 11 teeth. The total number of teeth should be as small as possible. [16] ?????

3

Code No: R5310304

III B.Tech I Semester(R05) Supplementary Examinations, May 2009 KINEMATICS OF MACHINERY (Mechanical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Two parallel shafts, with the distance between their axes being 20mm, are connected by an Oldham coupling. If the speed of the shafts is 400rpm, find the maximum speed of sliding of each tongue of the intermediate piece along its groove. (b) Find the distance between the fixed centers of a whit worth quick return motion mechanism if the length of driving link is 35mm, return stroke is 125mm and time ratio of cutting to return stroke is 1.75. [8+8] 2. (a) A coupler AB to form a simple Watt mechanism joins two bars OA and O1 B. When the mechanism is in its mean position, the lines OA and O1 B are perpendicular to AB. If OA=16cm, O1 B=24cm and AB=12cm, find the position of point P on connecting link which gives the best straight line motion. (b) Sketch and Describe the Scott-Russel and Robert’s straight-line motion mechanisms. [8+8] 3. (a) State and prove the Kennedy’s theorem as applicable to instantaneous centers of rotation of three bodies. How is it helpful in locating various instantaneous centers of a mechanism? (b) For the mechanism shown in Figure 1, determine the angular velocity of the link AB. OA=30 mm, AB=40 mm, QB=30 mm. [8+8]

Figure 1: 4. (a) What is a double Hooke’s joint? State the conditions to be satisfied in a double Hooke’s joint in order to provide a uniform velocity ratio through out a revolution. (b) The angle between the axes of two shafts connected by a Hooke’s joint is 22.5 degrees. The power supplied to the driving shaft is 7.5 KW at a uniform speed of 300 rpm. If the output torque on the driven shaft is not to vary by more than 15 percent of the input torque, what is the necessary moment of inertia of the flywheel? [6+10] 5. (a) Define pitch curve, pressure angle and base circle with reference to cams. (b) A reciprocating roller follower has cycloidal motion and its stroke of 30 mm is completed in 900 of the cam rotation. The follower is offset against the direction of rotation by 6.25 mm and the radius of the roller is 12.5mm. Determine the base circle radius which would limit the pressure angle to 300 . [16] 6. (a) What do you mean by undercutting of gears? (b) Two 200 involute spur gears mesh externally and give velocity ratio of 3. Module is 3mm and the addendum is equal to 1.1 module. If the pinion rotates at 120rpm, determine i. The minimum number of teeth on each wheel to avoid interference. ii. The number of pairs of teeth in contact. [16] 7. A leather belt 120mm wide and 6mm thick transmits power from a pulley 800mm diameter which rotates at 450rpm. The angle of lap is 1600 and coefficient of friction is 0.3. The mass of the belt is 1000kg/m3 and the stress is not to exceed 2.5MPa. Find the maximum power that can be transmitted. [16] 8. An epicyclic gear train consists of a compound gear wheel CD which gears with two internal wheels A and B. Gear wheel C has 30 teeth and meshes with internal wheel A while D gears with internal wheel B having 85 teeth. Internal wheel B is keyed to a shaft L. The compound wheel revolves freely on a pin which projects from a disc keyed to a shaft coaxial with L. (a) What is the speed of shaft L if shaft M makes 1000rpm and all the wheels have the same pitch? (b) What is the load torque on the shaft L and holding torque on wheel A if input torque to shaft M is 80kN.m. [16] ?????

4

Code No: R5310304

III B.Tech I Semester(R05) Supplementary Examinations, May 2009 KINEMATICS OF MACHINERY (Mechanical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) What is the difference between an element and a kinematic link of a machine? How do you classify links of a machine? (b) What do you mean by degree of freedom of a kinematics pair? How are pairs classified? Give examples. (c) Describe elliptical trammel. Show that it can describe a true ellipse? [5+6+5] 2. In the figure 1 shown OA and AC are the crank and connecting rod respectively. B is a point lying on the extension of AC. Find the length of the crank in order that the point B traverses approximately along a straight line when the connecting rod rotates from angle θ1 to angle θ2 . [16]

Figure 1: 3. In a slider-crank mechanism, the crank is 450 mm long and rotates at 30 rad/s in the counter-clockwise direction. The length of the connecting rod is 1.5 m. When the crank turns 30o from the inner-dead center, determine, (a) (b) (c) (d)

the the the the

velocity of the slider velocity of a point E located at a distance 450 mm on the connecting rod extended position and velocity of a point F on the connecting rod having the least absolute velocity angular velocity of the connecting rod.

[16]

4. (a) Sketch polar velocity diagram of a Hooke’s joint and mark its salient features. (b) The angle between the axes of two shafts joined by Hooke’s joint is 20o . The driving shaft rotates at a uniform speed of 200 rpm. The driven shaft carries a steady load corresponding to a power of 7.5 kW. Calculate the mass of the flywheel of the driven shaft if its radius of gyration is 160 mm and the output torque of the driven shaft does not vary by more than 12% of the input shaft. [6+10] 5. (a) Define the terms prime circle, pitch circle, base circle of a cam. (b) Draw the profile of a cam which is to give oscillatory motion to the follower with uniform angular velocity about its pivot. The base circle diameter is 50mm, angle of oscillation of the follower 300 and the distance between the cam centre and the pivot of the follower 60mm. The oscillating lever is 60mm long with a roller of 8mm diameter at the end. One oscillation of the follower is completed in one revolution of the cam. [16] 6. (a) Define path of contact of two gear wheels. (b) Two 200 involute gears in mesh have a gear ratio of 2 and 20 teeth on the pinion. The module is 5mm and the pitch line speed is 1.5 m/s. Assuming addendum to be equal to one module, find i. angle turned through by pinion when one pair of teeth is in mesh, and ii. maximum velocity of sliding. [16] 7. A pulley is driven by a flat belt 100mm wide and 6mm thick. The density of belt material is 1000 kg/m3 . The angle of lap is 1200 and the coefficient of friction 0.3. The maximum stress in the belt is not to exceed 2MPa. Find the maximum power that can be transmitted and the corresponding speed of the belt. [16] 8. An epicyclic gear train consists of a compound gear wheel CD which gears with two internal wheels A and B. Gear wheel C has 30 teeth and meshes with internal wheel A while D gears with internal wheel B having 85 teeth. Internal wheel B is keyed to a shaft L. The compound wheel revolves freely on a pin which projects from a disc keyed to a shaft coaxial with L. (a) What is the speed of shaft L if shaft M makes 1000rpm and all the wheels have the same pitch? (b) What is the load torque on the shaft L and holding torque on wheel A if input torque to shaft M is 80kN.m. [16] ?????