Kom Unit III

Unit III: Kinematics of Cam Mechanisms KOM

Unit III

Cam: A cam is a mechanical member used to impart desired motion to a follower by direct contact. The cam may be rotating or reciprocating whereas the follow may be rotating, reciprocating or oscillating. Complicated output motions (which are difficult to achieve) can be easily produced with the help of cam. Cams are widely used in automatic machines, internal combustion engine machine tools, printing control mechanisms, and so on. They are manufactured usually by die-casting, milling or by punch-presses.

A cam and the follower combination belong to the category of higher pair.

Necessary elements of a cam mechanism are: • A driver member known as the cam • A driven member called the follower • A frame which supports the cam and guides the follower.

Types of Cam:Cams are classified according to: I. Shape II. Follower movement, and III. Manner of constraint of the follower.

I. According to Shape: 1. Wedge and Flat Cams 2. Radial or Disc Cams 3. Spiral Cams 4. Cylindrical Cams 5. Conjugate Cams 6. Globoidal Cams 7. Spherical Cams

1. Wedge cam 2. Radial cam 3. Spiral Cams

4. Cylindrical cam 5.Conjugate cam

6. Globoidal cam 7.Spherical cam

Department of Mechanical, AAMEC Page 1


II. According to Follower Movement: 1. Rise-Return-Rise (R-R-R)2. Dwell-Rise-Return-Dwell (D-R-R-D)3. Dwell-Rise-Dwell-Return-Dwell (D-R-D-R-D)

1. R-R-R 2. D-R-R-D 3. D-R-D-R-D

III. According to Manner of Constraint of the Follower:1. Pre-loaded Spring Cam2. Positive-drive cam3. Gravity cam

1. Pre-loaded spring cam 2.Positive-drive cam 3.Gravity cam

Types of Followers: Cam followers are classified according to: I. Shape II. Movement, and III. Location of line of movement

I. According to Shape1. Knife-edge Follower2. Roller Follower

3. Mushroom Follower

1. Knife-edge follower 2.Roller follower 3.Mush-room follower (a) Flat-faced

II. According to Movement1. Reciprocating Follower2. Oscillating Follower

1. Reeciprocating follower 2.Oscillating follower

III. According to Location of Line of Movement1. Radial Follower2. Offset Follower

1. Radial Follower 2.Offset Follower


(b) Spherical-faced


DEFINITIONS:

Base Circle: It is the smallest circle tangent to the cam profile (contour) drawn from the centre of rotation of a radial cam.

Trace point: It is a reference point on the follower to trace the cam profile such as the knife-edge of a knife-edged follower and centre of the roller of a roller follower.

Pitch curve: It is the curve drawn by the trace point assuming that the cam is fixed, and the trace point of the follower rotates around the cam.

Pressure Angle: The pressure angle is angle between the normal to the pitch curve at a point and the direction of the follower motion. It represents the steepness of the cam profile. It varies in magnitude at all instants of the follower motion. A high value of the maximum pressure angle is not desired as it might jam the follower in the bearings.

Pitch point: It is the point on the pitch curve at which the pressure angle is maximum.

Pitch circle: It is the circle passing through the pitch point and concentric with the base circle.

Prime circle: The smallest circle drawn tangent to the pitch curve is known as the prime circle.

FOLLOWER DISPLACEMENT PROGRAMMING

Angle of Ascent (or) Angle of Rise (or) Angle of outstroke (θO): It is the angle through which the cam turns during the time the follower rises.

Angle of Dwell (θD): Angle of dwell is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.

Angle of Descent (or) Angle of Return (θR): It is the angle through which the cam turns during the time the follower returns to the initial position.

Angle of Action: Angle of action is the total angle moved by the cam during the time, between the beginning of rise and the end of the return of the follower.

To satisfy the given requirements of the follower displacement, a programme can be made keeping in view the following points: (i) In a given specific interval of time, due consideration to the velocity and the acceleration must be given. (ii) Cam Surface convex should be maintained optimum value to avoid follower lifting force.

(iii) The size of the base circle controls the pressure angle. As shown in Figure above the increase in the base circle diameter increases the length of the arc of the circle upon which the wedge (the raised portion) is to be made. A short wedge for a


Unit III: Kinematics of Cam Mechanisms KOMgiven rise requires a steep rise or a higher pressure angle, thus, increasing the lateral force.HIGH SPEEDCAMS: Force is always felt at the contact point of the follower with the cam surface and at the bearings. An acceleration curve with abrupt changes exerts abrupt stresses on the cam surfaces and at the bearings accompanied by detrimental effects such as surface wear and noise etc. All this may lead to an early failure of the cam system. Thus, it is very important to give due consideration to velocity and acceleration curves while choosing a displacement diagram. They should not have any step changes. In low-speed applications, cams with discontinuous acceleration characteristic may not show any undesirable characteristic, but at higher speeds such cams are certainly bound to show the same. The higher the speed, the higher is the need for smooth curves. At very high speeds, even the jerk (related to rate of change of acceleration or force) is made continuous as well. For most of the applications, however, this may not be needed.

UNDERCUTTING: Sometimes, it may happen that the prime circle of a cam is proportioned to provide a satisfactory pressure angle; still the follower may not be completing the desired motion. This can happen if the curvature of the pitch curve is too sharp.

Fig (a) shows the pitch curve of a cam. In Fig (b), a roller follower is shown generating this curve. In Fig.(c), a larger roller is shown trying to generate this curve. It can easily be observed that the cam curve loops over itself in order to realize the profile of the pitch curve. As it is impossible to produce such a cam profile, the result

is that the cam will be undercut become a pointed cam. Now, when the roller follower will be made to over this cam, it will not be producing the desired motion.

FOLLOWER MOTIONS:

The follower, during its travel, may have one of the following motions.1. Uniform velocity2. Simple harmonic motion3. Uniform acceleration and retardation,4. Cycloidal motion.

1. Uniform velocity:

The displacement, velocity and acceleration diagrams when a knife-edged follower moves with uniform velocity are shown in Fig. (a), (b) and (c) respectively. The abscissa (base) represents the time (i.e. the number of seconds required for the cam to complete one revolution) or it may represent the angular displacement of the cam in degrees. The ordinate represents the displacement, or velocity or acceleration of the follower.



2. Simple Harmonic Motion: The displacement, velocity and acceleration diagrams when the follower moves with simple harmonic motion are shown in Fig.(a), (b) and (c) respectively. The displacement diagram is drawn as follows : 1. Draw a semi-circle on the follower stroke as diameter. 2. Divide the semi-circle into any number of even equal parts (say eight). 3. Divide the angular displacements of the cam during out stroke and return stroke into the same number of equal parts. 4. The displacement diagram is obtained by projecting the points as shown in Fig.(a). The velocity and acceleration diagrams are shown in Fig. (b) and (c) respectively. Since the follower moves with a simple harmonic motion, therefore velocity diagram consists of a sine curve and the acceleration diagram is a cosine curve. Fig. (b) shows that the velocity of the follower is zero at the beginning and at the end of its stroke and increases gradually to a maximum at mid-stroke. On the other hand, the acceleration of the follower is maximum at the beginning and at the ends of the stroke and diminishes to zero at mid-stroke.

S = Stroke of the follower,θO and θR = Angular displacement of the cam during out stroke and return stroke of the follower respectively, in radians, andω= Angular velocity of the cam in rad/s.

Time required for the out stroke of the follower in seconds, tO θω Consider a point P moving at a uniform speed ωp radians per sec round the circumference of a circle with the stroke S as diameter, as shown in Fig.(d). The point P’ (which is the projection of a point P on the diameter) executes a simple harmonic motion as the point P rotates. The motion of the follower is similar to that of point P’. Peripheral speed of the point P’,

and maximum velocity of the follower on the outstroke,

We know that the centripetal acceleration of the point P,

Maximum acceleration of the follower on the outstroke,

Similarly, maximum velocity of the follower on the return stroke

and maximum acceleration of the follower on the return stroke,



3. Uniform acceleration and retardation: The displacement, velocity and acceleration diagrams when the follower moves with uniform acceleration and retardation are shown in Fig.(a), (b) and (c) respectively. The displacement diagram consists of a parabolic curve and may be drawn as discussed below: 1. Divide the angular displacement of the cam during outstroke ( θO ) into any even number of equal parts (say eight) and draw vertical lines through these points as shown in Fig.(a). 2. Divide the stroke of the follower (S) into the same number of equal even parts. 3. Join Aa to intersect the vertical line through point 1 at B. Similarly, obtain the other points C, D etc. as shown in Fig. (a). Now join these points to obtain the parabolic curve for the out stroke of the follower. 4. In the similar way as discussed above, the displacement diagram for the follower during return stroke may be drawn. Since the acceleration and retardation are uniform, therefore the velocity varies directly with the time. The velocity diagram is shown in Fig. (b).

S = Stroke of the follower, θO and θR = Angular displacement of the cam during out stroke and return stroke of the follower respectively, and ω= Angular velocity of the cam. We know that time required for the follower during outstroke, tO θωand time required for the follower during return stroke, tR θR /ωMean velocity of the follower during outstroke = S/tO

and mean velocity of the follower during return stroke = S/tR

Since the maximum velocity of follower is equal to twice the mean velocity, therefore maximum velocity of the follower during outstroke,

Similarly, maximum velocity of the follower during return stroke,

From acceleration diagram as shown in Figure (c), that during first half of the outstroke there is uniform acceleration and during the second half of the out stroke there is uniform retardation. Thus, the maximum velocity of the follower is reached after the time tO / 2 (during outstroke) and tR /2 (during return stroke).

Maximum acceleration of the follower during outstroke,



Similarly, maximum acceleration of the follower during return stroke,

4. Cycloidal motion.

The displacement, velocity and acceleration diagrams when the follower moves with cycloidal motion are shown in Fig. (a), (b) and (c) respectively. We know that cycloid is a curve traced by a point on a circle when the circle rolls without slipping on a straight line. In case of cams, this straight line is a stroke of the follower which is translating and the circumference of the rolling circle is equal to the stroke (S) of the follower. Therefore the radius of the rolling circle is S / 2π. The displacement diagram is drawn as discussed below:

1. Draw a circle of radius S / 2π with A as centre.2. Divide the circle into any number of equal even parts (say six). Project these points horizontally on the vertical centre line of the circle. These points are shown by a’ and b’ in Fig. (a).3. Divide the angular displacement of the cam during outstroke into the same number of equal even parts as the circle is divided. Draw vertical lines through these points.4. Join AB which intersects the vertical line through 3′ at c. From a′ draw a line parallel to AB intersecting the vertical lines through 1′ and 2′ at a and b respectively.5. Similarly, from b′ draw a line parallel to AB intersecting the vertical lines through 4′ and 5′ at d and e respectively.6. Join the points A a b c d e B by a smooth curve. This is the required cycloidal curve for the follower during outstroke.

θ = Angle through which the cam rotates in time t seconds, andω = Angular velocity of the cam.

We know that displacement of the follower after time t seconds,

-------------(i)

Velocity of the follower after time t seconds,

----------------(ii)

The velocity is maximum, when

(or) (or)

Substituting θ= θO /2 in equation (ii), we have maximum velocity of the follower during outstroke,

Similarly, maximum velocity of the follower during return stroke,

Now, acceleration of the follower after time t sec,



---------------(iii)

The acceleration is maximum, when

(or) (or)

Substituting θθO/ 4 in equation (iii), we have maximum acceleration of the follower during outstroke,

Similarly, maximum acceleration of the follower during return stroke,

Procedure for Drawing Cam Profile:

The following procedure may be followed to draw the cam profile1. Draw the displacement diagram for follower motion2. Consider that cam remains stationary and that the follower moves round it in a direction opposite to the direction of cam rotation.3. Draw the cam base circle and divide its circumference into number of divisions depending upon the divisions used in the displacement diagram.4. Draw various positions of follower with dotted lines corresponding to different angular displacement from the radius from which ascent is to commence.5. Draw a smooth curve tangential to the contact surface in different position.

1. A cam is to give the following motion to a knife-edged follower:• Outstroke during 60° of cam rotation ; • Dwell for the next 30° of cam rotation ;• Return stroke during next 60° of cam rotation, and • Dwell for the remaining 210° of cam rotation.

The stroke of the follower is 40 mm and the minimum radius of the cam is 50 mm. The follower moves with uniform velocity during both the outstroke and return strokes. Draw the profile of the cam when: (a) the axis of the follower passes through the axis of the cam shaft, and (b) the axis of the follower is offset by 20 mm from the axis of the cam shaft.

Given data:

Cam lift S = 40 mm = 0.04 m; Angle of accent θO = 60° Dwell angle θD1 = 300 Angle of decent θR = 60° Dwell angle θD2 = 2100 Offset distance = 20 mm

Solution:

Displacement diagram:



(a) The axis of the follower passes through the axis of the cam shaft

(b) The axis of the follower is offset by 20 mm from the axis of the cam shaft.

2. A cam is to be designed for a knife edge follower with the following data: 1. Cam lift = 40 mm during 90° of cam rotation with simple harmonic motion. 2. Dwell for the next 30° 3. During 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 (a) The line of stroke of the follower passes through the axis of the cam shaft, and (b) 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 rpm.

Given: Cam lift S = 40 mm = 0.04 m; Angle of accent θO = 90° = π /2 rad = 1.571 rad ;Dwell angle θD1 = 300 = π /6 rad = 0.524 rad;

Angle of decent θR = 60° =π /3 rad = 1.047 rad ; Dwell angle θD2 = 1800 = π rad = 3.14 rad;Speed N = 240 r.p.m;

Solution:


Unit III: Kinematics of Cam Mechanisms KOMDisplacement diagram:

(a) The line of stroke of the follower passes through the axis of the cam shaft:

(b) The line of stroke is offset 20 mm from the axis of the cam shaft.

Maximum velocity of the follower during its ascent and descentWe know that angular velocity of the cam,

We also know that the maximum velocity of the follower during its ascent,

Maximum velocity of the follower during its descent,

Maximum acceleration of the follower during its ascent and descent:We know that the maximum acceleration of the follower during its ascent,

Maximum acceleration of the follower during its descent,



3. A cam, with a minimum radius of 25 mm, rotating 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 (a) The line of stroke of the valve rod passes through the axis of the cam shaft, b) The line of the stroke is offset 15 mm from the axis of the cam shaft. The displacement of the valve, while being raised and lowered, is to take place with simple harmonic motion. Determine the maximum acceleration of the valve rod when the cam shaft rotates at 100 rpm. Draw the displacement, the velocity and the acceleration diagrams for one complete revolution of the cam.Given : S = 50 mm = 0.05 m; θO = 120°= 2 π /3 rad = 2.1 rad ;θR = 60° =π /3 rad = 1.047 rad ; N = 100 rpm

Solution:


Velocity diagram:

Acceleration diagram:

Cam profile: (a) The line of stroke of the valve rod passes through the axis of the cam shaft


Unit III: Kinematics of Cam Mechanisms KOMThe line of the stroke is offset 15 mm from the axis of the cam shaft.

Maximum acceleration of the valve rodWe know that angular velocity of the cam shaft,

We also know that maximum velocity of the valve rod to raise valve,

Maximum velocity of the valve rod to lower the valve,

The velocity diagram for one complete revolution of the cam is shown in Figure

We know that the maximum acceleration of the valve rod to raise the valve,

Maximum acceleration of the valve rod to lower the valve,

4. A cam drives a flat reciprocating follower in the following manner: During 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.

Given data: Angle of ascent = 1200

Angle of first dwell = 300

Angle of descent = 1200

Angle of second dwell = 900

Base circle radius of the cam (minimum radius) = 25 mm Lift = 20mm

Solution:Displacement diagram:

Cam profile:



5. A cam, with a minimum radius of 50 mm, rotating 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 (i) When the line of stroke of the follower passes through the centre of the cam shaft, and (ii) 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. Determine the maximum velocity and acceleration of the follower when the cam shaft rotates at 900 rpm. Draw the displacement, velocity and acceleration diagrams for one complete revolution of the cam.

Given:

S = 40 mm = 0.04 m; θo =100° = 100 × π/180 = 1.745 rad;

θR = 90° =π/2 = 1.571 rad; N = 900 rpm.


Velocity diagram:

Acceleration diagram:



(i)Cam profile with line of stroke of the follower passes through the centre of the cam shaft:

(ii) Profile of the cam when the line of stroke of the follower is offset by 15 mm

Maximum velocity of the follower during out stroke and return strokeWe know that angular velocity of the cam shaft,

We also know that the maximum velocity of the follower during out stroke,

and maximum velocity of the follower during return stroke,

Maximum acceleration of the follower during out stroke and return strokeWe know that the maximum acceleration of the follower during out stroke,

and maximum acceleration of the follower during return stroke,

6. Design a cam for operating the exhaust valve of an oil engine. It is required to give equal uniform acceleration and retardation during opening and closing of the valve each of which corresponds to 60° of cam rotation. The valve must remain in the fully open position for 20° of cam rotation.


Unit III: Kinematics of Cam Mechanisms KOM The lift of the valve is 37.5 mm and the least radius of the cam is 40 mm. The follower is provided with a roller of radius 20 mm and its line of stroke passes through the axis of the cam.

Given data:Angle of ascent (valve open) = 600

Angle of dwell (maintain the valve open) = 200

Angle of decent (valve close) = 600

Lift of valve = 37.5 mmLeast radius of the cam (Base circle radius) = 40 mmRoller radius = 20 mm


7. Draw the profile of the cam when the roller follower moves with cycloidal motion during out stroke and return stroke, as given below: 1. Outstroke 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.

Given data: Angle of ascent (angle for outstroke) = 1800

Angle of decent (angle for return stroke) = 1500

Angle of dwell = 300 Minimum radius of cam (Base circle radius) = 15mm Roller diameter = 10mm Offset (Right side of the cam shaft) = 10mm


Radius of generating circle = = 5mm



Cam profile:

8. Construct the profile of a cam to suit the following specifications: 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; Numbers of pauses are two of equal interval between motions. During the lift, the motion is S.H.M. During the fall the motion is uniform acceleration and deceleration. The speed of the cam shaft is uniform. The line of stroke of the follower is off-set 12.5 mm from the centre of the cam.Solution:Displacement diagram:

Cam profile:

9. Draw the profile of a cam operating a roller reciprocating follower and with the following data:Minimum radius of cam = 25mmLift = 30mm;Roller diameter = 15mm; The cam lifts the follower for 1200 with SHM followed by a dwell period of 300

Then the follower lowers down during 1500 of the cam rotation with uniform acceleration and deceleration followed by a dwell period. If the cam rotates at a uniform speed of 150 rpm, calculate the maximum velocity and acceleration of the follower during the descent period.




Cam profile:

Maximum velocity of the follower during out stroke and return strokeWe know that angular velocity of the cam shaft,

We also know that the maximum velocity of the follower during return stroke,

Maximum acceleration of the follower during return stroke,



Part-A1. What are the major types of cams? (May/June 2013, R2008/2010)2. State the advantages of cam mechanisms-over linkage mechanisms. (May/June 2013, R2004/2007)3. Define Angle of dwell (May/June 2013, R2008/2010)4. Define undercutting in a cam mechanism. (May/June 2013, R2004/2007)5. Under what conditions, does a cam get undercut? (Nov/Dec 2013, R2004/2007)6. Define pressure angle. (Nov/Dec 2013, R2008/2010) [Define the term 'Pressure Angle' of a cam mechanism. (Nov/Dec2014, R2004/07)]7.Why large pressure angle is not preferred for cam curves?(May/June2012, R2008)8. What are the different motions of the follower? (May/June 2014, R2008/2010)

9. How the maximum velocity of the follower of a cam mechanism is found out during the lift which takes place with Simple Harmonic Motion? (Nov/Dec 2014, R2004/2007)10. State the expressions for maximum acceleration of a followers moving with cycloidal motion. (Nov/Dec 2012, R2008)11. List the advantages and limitations of a mushroom follower. (Nov/Dec 2013, R2004/2007)12. Why sometimes the axes of the translating roller followers in cam follower mechanisms are offset from the axis of rotation of the cam? (Nov/Dec 2012, R2008)13. Write the procedure to draw the cam profile. (Nov/Dec 2013, R2008/2010)14. Define tangent cam (May/June 2014, R2008/2010)

Part-B

1. (i)Sketch a plate cam mechanism with roller follower and mark. (8) (1) Pitch curve(2) Cam profile(3) Base circle(4) Prime circle(5) Rise(6) Return(7) Dwell.(ii) Derive equation of motion and its derivatives for a tangent cam with roller follower on straight surface. (8) (Nov/Dec 2014, R2004/2007)

2. A cam is to be designed for a knife edge follower with the following data: (i)Cam lift = 40 mm during 90° of cam rotation with simple harmonic motion. (ii)Dwell for the next 30°. (iii)During the next 60° of cam rotation, the follower returns to its original position with simple harmonic motion. (iv)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. (May/June 2014, R2008/2010)

3. A cam with a minimum radius of 25 mm is to be designed for a knife-edge follower with the following data:

To raise the follower through 35 mm during 60° rotation of the cam Dwell for next 40° of the cam rotation Descending of the follower during the next 90° of the cam rotation


Unit III: Kinematics of Cam Mechanisms KOM Dwell during the rest of the cam rotation

Draw the profile of the cam if the ascending and descending of the cam is with simple harmonic motion and the line of stroke of the follower is offset 10 mm from the axis of the cam shaft. Determine the maximum velocity and acceleration of the follower during the ascent and descent if the cam rotates at 150 rpm. (Nov/Dec 2013, R2004/2007)

4. A cam is to be designed for a knife edge follower with the following data: (i) Cam lift = 40 mm during 90° of cam rotation with simple harmonic motion. (ii) Dwell for the next 30°. (iii)During the next 60° of cam rotation, the follower returns to its original position with simple harmonic motion. (iv)Dwell during the remaining 180°.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.

(a) Draw the displacement diagram (b) Draw the profile of the cam(c) Determine the maximum velocity and acceleration of the follower during its

ascent and descent, if the cam rotates at 200 rpm in clockwise direction. (May/June 2012, R2008)

5. A cam with a minimum radius of 25mm, rotating clockwise at a uniform speed is to be designed to give motion to a roller follower, at the end of a valve rod, as described below:(a)To raise the valve through 50mm during 1200 rotation of the cam(b)To keep the valve fully raised through next 300

(c)To lower the valve during next 600 and(d)To keep the valve closed during rest of the revolutionThe diameter of the roller is 20mm and the diameter of the cam shaft is 25mm.The line of the stroke is offset by 15mm from the axis of the cam shaft. The displacement of the valve, while being raised and lowered is to take place with SHM(1)Draw the displacement diagram. Sketch roughly the shapes of velocity and acceleration diagrams.(2)Draw the profile of the cam (Nov/Dec 2012, R2008)

6. Draw the profile of cam when the follower moves the cycloidal motion for both out stroke and return stroke as detailed below.(i) Outstroke with maximum displacement of 48 mm during 1800 of cam rotation.(ii) Return stroke for the next 1000 of cam rotation.(iii) Dwell for the remaining period.

The minimum radius of the cam is 30 mm and diameter of roller is 15 mm. The axis of the follower passes through the axis of the cam shaft.(Nov/Dec 2014, R2004/2007)

7. A cam operates on offset roller follower. The least radius of the cam is 50mm, roller diameter is 30 mm, and offset is 20 mm, the cam rotates at 360rpm. The angle of ascent is 48°, angle of dwell is 42°, and angle of descent is 60°. The motion is to be SHM during ascent and uniform acceleration and deceleration during decent. Draw the cam profile. (16)(Nov/Dec 2013, R2008/2010)

8. Draw the profile of a cam in which the follower moves with simple harmonic motion during rise while it moves with uniform acceleration and retardation motion during return, from the following data:Least radius of cam = 50mmAngle of rise = 88°Angle of return = 80°Offset of the follower = 20mm rightLift of the follower = 40mmAngle of dwell between rise = 72°If the cam rotates at 360 rpm clockwise find the maximum velocity during return. (May/June 2013, R2004/2007)

9. A cam with a minimum radius of 25mm, rotating clockwise at uniform speed of 300 rpm is to the designed to give motion to a flat faced mushroom follower as detailed below:(i)To raise through a distance of 25 mm in 1200 rotation of the cam(ii) To remain at rest for the next 300

(iii) To lower during further 1200rotation of the cam(iv) To remain in the same position during rest of the revolution.The raising of the follower takes place with cycloidal motion and the lowering with uniform acceleration and retardation. However, the uniform acceleration is 2/3rd of the uniform retardation. Draw the displacement diagram and profile of the cam. (May/June 2013, R2008/2010)

10. A circular cam operating a flat faced follower has a least diameter of 40mm. The lift is 12mm and angle of action is 1600. The Speed of rotation is 500 rpm. If the period of acceleration of the follower is 60%of the retardation during the lift, determine the following: (i)The principal dimensions of the cam


Unit III: Kinematics of Cam Mechanisms KOM(ii)The acceleration at the main points.Also determine the maximum acceleration and deceleration during the lift.(May/June 2013, R2008/2010)

11. A tangent cam with a base circle diameter of 50mm operates a roller follower 20 mm in diameter. The line of stroke of the roller follower passes through the axis of the cam. The angle between the tangential faces of the cam is 60°, speed of the cam shaft 200 rpm and the lift of the follower 15mm. Calculate:(i) The main dimensions of the cam (6)(ii) The accelerations of the follower at (10) (1) The beginning of lift (2) Where the roller just touches the nose (3) The apex of the circular nose. (May/June 2013, R2004/2007)

12. (i) A flat faced mushroom follower is operated by a symmetrical cam with circular arc flank and nose profile the axis of tappet passed through the cam axis. Total angle of action is 162°, lift 10 mm and base circle diameter 40mm. period of acceleration is half the period of retardation during the lift. The cam rotates at 1200 rpm.Determine (1) The nose and flank radii and (2) The maximum acceleration and retardation during lift. (12)

(ii) List the various methods to be used to reduce the pressure angle: (4) (Nov/Dec 2013, R2008/2010)

13. A symmetrical circular cam operating a flat-faced follower has the following particulars: Minimum radius of cam =50 mm; Total lift =30 mm; Angle of lift =80°; Nose radius =12 mm; Speed= 210 rpm; Find(i) The principal dimensions of the cam. (8)(ii) The acceleration of the follower at the beginning of the lift, at the end of contact with the circular flank, at the beginning of contact with nose and at the apex of the nose. (8) (Nov/Dec 2013, R2004/2007)

14. The following particulars relate to a symmetrical circular cam operating a flat faced follower: Least radius=25mm, Nose radius=8mm, Lift of the valve=10mm, Angle of action of the cam=1200, cam shaft speed=1000rpm.(i)Find the flank radius

(ii)Determine the maximum values of velocity, acceleration and retardation of the follower(iii)Draw the profile of the cam (May/June 2012, R2008)

15. In a symmetrical tangent cam operating a roller follower, the least radius of the cam is 30mm and roller radius is 17.5mm. The angle of ascent is 750 and the total lift is 17.5mm. The speed of the cam shaft is 600rpm. Assume that there is no dwell between ascent and descent.(i) Calculate the principle dimension of the cam(ii)Find the acceleration of the follower at the beginning of the lift(iii)Draw the profile of the cam (Nov/Dec 2012, R2008)

16. In a cam translating follower, the follower axis is offset to the right of cam hinge by 12mm.The roller radius is 10mm and the cam rotates in the counter clock-wise direction. Layout the rise portion of the cam profile to meet the follower specifications: Rise takes place during 1800 of the cam rotation of which for the first 900 the rise is with constant acceleration and rest is with constant retardation. Take seven station points only. The lift of the cam is 30mm and the least radius of the cam is 25 mm.(May/June 2014, R2008/2010)


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Kom Unit III