Solved problems based on CAM Profiles | Kinematics of Machines Tutorials

Solved problems based on CAM Profiles

Cam is a very important topic in the kinematics of machines or theory of machines. Here we are presenting some solved problems based on cam profiles. Although we checked the errors, but if you mark some error, let us known in the comment box.

(1) Draw the cam profile for following conditions:

Follower type = Knife edged, in-line; lift = 50mm; base circle radius = 50mm; out stroke with SHM, for 600 cam rotation; dwell for 450 cam rotation; return stroke with SHM, for 900 cam rotation; dwell for the remaining period. Determine max. velocity and acceleration during out stroke and return stroke if the cam rotates at 1000 rpm in clockwise direction.

Displacement diagram:

Cam Solved Problems

Cam profile: Construct base circle. Mark points 1,2,3…..in direction opposite to the direction of cam rotation. Transfer points a,b,c…..l from displacement diagram to the cam profile and join them by a smooth free hand curve. This forms the required cam profile.

 

problems based on CAM

Calculations:

Angular velocity of cam = clip_image006=104.76 rad/sec

 

Max. velocity of follower during outstroke = vomax = clip_image008=

= clip_image010 =7857mm/sec =7.857m/sec

Similarly Max. velocity of follower during return stroke = , vrmax = clip_image012 =

= clip_image014 = 5238mm/sec = 5.238m/sec

 

Max. acceleration during outstroke = aomax = rω2p (from d3) = clip_image016 =

= clip_image018 2469297.96mm/sec2 = 2469.3m/sec2

 

Similarly, Max. acceleration during return stroke = armax = clip_image020 =

= clip_image022 1097465.76mm/sec2 = 1097.5m/sec2

 

 


 

(2) Draw the cam profile for the same operating conditions of problem (1), with the follower off set by 10 mm to the left of cam center.

Displacement diagram: Same as previous case.

 

Cam profile: Construction is same as previous case, except that the lines drawn from 1,2,3…. are tangential to the offset circle of 10mm dia. as shown in the fig.

problems based on CAM

 

 

 

(3) Draw the cam profile for following conditions:

Follower type = roller follower, in-line; lift = 25mm; base circle radius = 20mm; roller radius = 5mm; out stroke with UARM, for 1200 cam rotation; dwell for 600 cam rotation; return stroke with UARM, for 900 cam rotation; dwell for the remaining period. Determine max. velocity and acceleration during out stroke and return stroke if the cam rotates at 1200 rpm in clockwise direction.

Displacement diagram:

clip_image026

 

Cam profile: Construct base circle and prime circle (25mm radius). Mark points 1,2,3…..in direction opposite to the direction of cam rotation, on prime circle. Transfer points a,b,c…..l from displacement diagram. At each of these points a,b,c… draw circles of 5mm radius, representing rollers. Starting from the first point of contact between roller and base circle, draw a smooth free hand curve, tangential to all successive roller positions. This forms the required cam profile.

 

clip_image028

 

Calculations:

Angular velocity of the cam = clip_image030125.71rad/sec

 

Max. velocity during outstroke =clip_image032 =

= clip_image0342999.9mm/sec =2.999m/sec

 

Max. velocity during return stroke = clip_image036

= 3999.86mm/sec = 3.999m/sec

 

Acceleration of the follower during outstroke = clip_image038 =

= clip_image040359975mm/sec2 = 359.975m/sec2

 

Similarly acceleration of the follower during return stroke = clip_image042 =

= clip_image044639956mm/sec2 = 639.956m/sec2

 

 

 


(4) Draw the cam profile for conditions same as in (3), with follower off set to right of cam center by 5mm and cam rotating counter clockwise.

Displacement diagram: Same as previous case.

 

Cam profile: Construction is same as previous case, except that the lines drawn from 1,2,3…. are tangential to the offset circle of 10mm dia. as shown in the fig.

clip_image046

(5) Draw the cam profile for following conditions:

Follower type = roller follower, off set to the right of cam axis by 18mm; lift = 35mm; base circle radius = 50mm; roller radius = 14mm; out stroke with SHM in 0.05sec; dwell for 0.0125sec; return stroke with UARM, during 0.125sec; dwell for the remaining period. During return stroke, acceleration is 3/5 times retardation. Determine max. velocity and acceleration during out stroke and return stroke if the cam rotates at 240 rpm.

Calculations:

Cam speed = 240rpm. Therefore, time for one rotation = clip_image048

Angle of out stroke = clip_image050

Angle of first dwell = clip_image052

Angle of return stroke = clip_image054

Angle of second dwell = clip_image056

Since acceleration is 3/5 times retardation during return stroke,

clip_image058 (from acceleration diagram) clip_image060

 

But clip_image062

 

Displacement diagram is constructed by selecting ta and tr accordingly.

clip_image064

Angular velocity of cam = clip_image066=25.14 rad/sec

 

Max. velocity of follower during outstroke = vomax = clip_image008[1]=

= clip_image068 = 1099.87mm/sec =1.1m/sec

 

Similarly Max. velocity during return stroke = clip_image070

= 559.9 mm/sec = 0.56m/sec

 

Max. acceleration during outstroke = aomax = rω2p (from d3) = clip_image016[1] =

= clip_image072 69127.14mm/sec2 = 69.13m/sec2

 

acceleration of the follower during return stroke = clip_image074 = 7166.37 mm/sec2 = 7.17m/sec2

 

similarly retardation of the follower during return stroke = clip_image076 = 11943.9 mm/sec2 = 11.94m/sec2

 

clip_image078

 

 

(6) Draw the cam profile for following conditions:

Follower type = knife edged follower, in line; lift = 30mm; base circle radius = 20mm; out stroke with uniform velocity in 1200 of cam rotation; dwell for 600; return stroke with uniform velocity, during 900 of cam rotation; dwell for the remaining period.

Displacement diagram:

clip_image080

Cam profile:

clip_image082

 

 

(7) Draw the cam profile for following conditions:

Follower type = oscillating follower with roller as shown in fig.; base circle radius = 20mm; roller radius = 7mm; follower to rise through 400 during 900 of cam rotation with cycloidal motion; dwell for 300; return stroke with cycloidal motion during 1200 of cam rotation; dwell for the remaining period. Also determine the max. velocity and acceleration during outstroke and return stroke, if the cam rotates at 600 rpm.

clip_image084clip_image086

Lift of the follower = S = length AB clip_image088 arc AB = clip_image090 = 53 mm.

Radius of cycloid generating circle = clip_image092 = 8.4 mm

Displacement diagram;

clip_image094

Angular velocity of cam = clip_image096 = 62.86 rad/sec

 

vomax = Max. velocity of follower during outstroke = clip_image098 = 4240.2 mm/sec

 

vrmax = Max. velocity of follower during return stroke = clip_image100 = 3180 mm/sec

 

aomax = Max. acceleration during outstroke =

clip_image102 = 533077 mm/sec2

 

= 533.1 m/sec2.

 

armax = Max. acceleration during return stroke =

clip_image104 = 299855.8mm/sec2 = 299.8 m/sec2.

 

Cam profile: Draw base circle and prime circle. Draw another circle of radius equal to the distance between cam center and follower pivot point. Take the line joining cam center and pivot point as reference and draw lines indicating successive angular displacements of cam. Divide these into same number of divisions as in the displacement diagram. Show points 1’, 2’, 3’… on the outer circle. With these points as centers and radius equal to length of follower arm, draw arcs, cutting the prime circle at 1,2,3…. Transfer points a,b,c.. on to these arcs from displacement diagram. At each of these points a,b,c… draw circles of 7mm radius, representing rollers. Starting from the first point of contact between roller and base circle, draw a smooth free hand curve, tangential to all successive roller positions. This forms the required cam profile.

clip_image106

 

(8) Draw the cam profile for following conditions:

Follower type = knife edged follower, in line; follower rises by 24mm with SHM in 1/4 rotation, dwells for 1/8 rotation and then raises again by 24mm with UARM in 1/4 rotation and dwells for 1/16 rotation before returning with SHM. Base circle radius = 30mm.

Angle of out stroke (1) = θ01 = clip_image108

Angle of dwell (1) = clip_image110

Angle of out stroke (2) = θ02 = clip_image108[1]

 

Angle of dwell (2) = clip_image113

 

Angle of return stroke = θr = clip_image115

Displacement diagram:

clip_image117

Cam profile:

clip_image119

 

(9) Draw the cam profile for following conditions:

Follower type = flat faced follower, in line; follower rises by 20mm with SHM in 1200 of cam rotation, dwells for 300 of cam rotation; returns with SHM in 1200 of cam rotation and dwells during the remaining period. Base circle radius = 25mm.

Displacement diagram:

clip_image121

Cam profile: Construct base circle. Mark points 1,2,3…..in direction opposite to the direction of cam rotation, on prime circle. Transfer points a,b,c…..l from displacement diagram. At each of these points a,b,c… draw perpendicular lines to the radials, representing flat faced followers. Starting from the first point of contact between follower and base circle, draw a smooth free hand curve, tangential to all successive follower positions. This forms the required cam profile.

clip_image123

 

(10) Draw the cam profile for following conditions:

Follower type = roller follower, in line; roller dia. = 5mm; follower rises by 25mm with SHM in 1800 of cam rotation, falls by half the distance instantaneously; returns with Uniform velocity in 1800 of cam rotation. Base circle radius = 20m.

Displacement diagram:

clip_image125

Cam profile:

clip_image127

 

 

(11) Draw the cam profile for following conditions:

Follower type = roller follower, off-set to the right by 5mm; lift = 30mm; base circle radius = 25mm; roller radius = 5mm; out stroke with SHM, for 1200 cam rotation; dwell for 600 cam rotation; return stroke during 1200 cam rotation; first half of return stroke with Uniform velocity and second half with UARM; dwell for the remaining period.

Displacement diagram:

clip_image129

Cam profile:

clip_image131

 

 

(12) A push rod of valve of an IC engine ascends with UARM, along a path inclined to the vertical at 600. The same descends with SHM. The base circle diameter of the cam is 50mm and the push rod has a roller of 60mm diameter, fitted to its end. The axis of the roller and the cam fall on the same vertical line. The stroke of the follower is 20mm. The angle of action for the outstroke and the return stroke is 600 each, interposed by a dwell period of 600. Draw the profile of the cam.

Displacement diagram:

clip_image133

Cam profile:

clip_image135

29 Responses to “Solved problems based on CAM Profiles | Kinematics of Machines Tutorials”

  1. Adenaya Demilade

    Wow!!!The solved examples has helped me a lot. Now I see how the whole thing really is…. thanks guys

  2. admin

    Thanks for the appreciation

  3. priya

    Grt…!! Was quite helpful

  4. admin

    Thanks, comment more if you need anything else.

  5. ivan

    guys i need help! a cam is required for an automated transfer mechanism. The cam follower must rise outward 1.0 inch with constant velocity in 3.0 seconds, dwell for 0.5 seconds, fall with constant velocity 2.0 seconds, and then repeat the sequence. Determine the required speed of the cam.

  6. admin

    Hello,

    one rotation in 5.5 second
    In one second, the cam rotates 1/5.5 times
    In one minute, the cam rotates for 60/5.5 times

    So the speed in rpm would be 10.90 rpm

    However, if you rest the cam after the function that is second dwell for 0.5 seconds, You need 10 rpm.

    Precisely, I think you need cam profile.

    Enjoy!!

  7. SHUBHAM

    A cam with a minimum radius of 25 mm,
    rotating in clockwise direction with a uniform
    speed
    of 100 rpm is to be designed to give the motion for
    a roller follower as follows.
    (i) To raise through 50
    mm during 120° rotat
    ion of cam with SHM. (ii)
    Fully raised through
    next 30°. (iii) To lower during
    next 60° with UAUR. (iv) Dwell for the remaining
    period.
    Draw the profile of the cam when the line of
    stroke of the follower is offset by 15 mm from
    the
    axis of the camshaft……..I need the solution of ths

  8. admin

    Thanks for the comment.

    Will try to get a solution and mail u.

  9. Ishan

    Awesome examples!Thanks

  10. admin

    Thanks for the appreciation.

  11. Anyewi George

    good constructions

  12. Daniel Amine

    I found this very useful in preparing for my classes.
    Best wishes

  13. admin

    Thanks. Please send feedback/suggestions for improvement.

  14. Chinmay

    Need to know the scheme of valuation of the cam .plz.

  15. Nikhil

    If speed is given is counter clockwise than how to draw profile of cam

  16. SITHIVINAYAGAM N

    sir its fantastic work, only one help sir may i get copy of work to my mailid. Pls

  17. Madhu

    Sir how can we divide the 6 equal part of outstroke and return stroke. If we have 60° outstroke and 90° return stroke then how can I divide both of them in 6 equal parts . please solve it and inform me .

  18. Yusuf musa

    I spend a lot of my time for preparing my Classes

  19. juny

    it is very helpful to my subject. sir can i ask a pdf copy for this in my email because our internet connection here is very limited?

  20. admin

    Thanks for liking it.

    I will try to send an email to your mail.

    Thanks again.

  21. BALASUBRAMANIAN

    Draw the profile of a cam to give the following motion to a roller follower; Output stroke during 50 of cam rotation, dwell for 10 of cam rotation, return stroke during 50 of cam rotation and dwell for the remaining 250 of cam rotation. The stroke of the follower is 2.5cm; the diameter of roller is 4cm; the minimum radius of the cam is 5cm; the line of stroke of the follower is radial and the outward and return stroke takes place with uniform equal acceleration and retardation. pls solve the problems

  22. admin

    Thanks for the comment. It is not possible for me to explain here. But I will try.

  23. Nishigandha

    I want to design a cylindrical cam and follower mechanism.Can you help me with the force calculations.??

  24. admin

    Sure, Will pass this on. Someone will definitely do.

  25. K. Manimaran

    Sir I need tangent cam and circular arm notes……… Plz help me sir

  26. K. Manimaran

    How to draw tangent cam profile diagram?

  27. Tifany

    This is very helpful information you provided. Thank you.Can we have it in the form of aPdf as well

  28. Gaurav

    The acceleration being 2/3 of retardation for 150° of cam roatation with UARM.

  29. Sudarshan

    Please give solution for this problem

    Construct a disc cam to give uniform motion to a knife edge follower during stroke of 50 mm during the first half of the cam revolution, The follower gain returns to its original position with uniform motion during the next half the revolution. The minimum radius of the cam is 50 mm and the diameter e can shaft is 35 mm. Draw the profile of the cam when the axis of passes through the axis of cam shaft.

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