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 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.

 

Calculations:

Angular velocity of cam = =104.76 rad/sec

 

Max. velocity of follower during outstroke = vo_max = =

= =7857mm/sec =7.857m/sec

Similarly Max. velocity of follower during return stroke = , vr_max = =

= = 5238mm/sec = 5.238m/sec

 

Max. acceleration during outstroke = ao_max = rω²_p (from d3) = =

= 2469297.96mm/sec² = 2469.3m/sec²

 

Similarly, Max. acceleration during return stroke = ar_max = =

= 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.

 

 

 

(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:

 

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.

 

 

Calculations:

Angular velocity of the cam = 125.71rad/sec

 

Max. velocity during outstroke = =

= 2999.9mm/sec =2.999m/sec

 

Max. velocity during return stroke =

= 3999.86mm/sec = 3.999m/sec

 

Acceleration of the follower during outstroke = =

= 359975mm/sec² = 359.975m/sec²

 

Similarly acceleration of the follower during return stroke = =

= 639956mm/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.

(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 =

Angle of out stroke =

Angle of first dwell =

Angle of return stroke =

Angle of second dwell =

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

(from acceleration diagram)

 

But

 

Displacement diagram is constructed by selecting t_a and t_r accordingly.

Angular velocity of cam = =25.14 rad/sec

 

Max. velocity of follower during outstroke = vo_max = =

= = 1099.87mm/sec =1.1m/sec

 

Similarly Max. velocity during return stroke =

= 559.9 mm/sec = 0.56m/sec

 

Max. acceleration during outstroke = ao_max = rω²_p (from d3) = =

= 69127.14mm/sec² = 69.13m/sec²

 

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

 

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

 

 

 

(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:

Cam profile:

 

 

(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.

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

Radius of cycloid generating circle = = 8.4 mm

Displacement diagram;

Angular velocity of cam = = 62.86 rad/sec

 

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

 

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

 

ao_max = Max. acceleration during outstroke =

= 533077 mm/sec²

 

= 533.1 m/sec².

 

ar_max = Max. acceleration during return stroke =

= 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.

 

(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 =

Angle of dwell (1) =

Angle of out stroke (2) = θ₀₂ =

 

Angle of dwell (2) =

 

Angle of return stroke = θ_r =

Displacement diagram:

Cam profile:

 

(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:

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.

 

(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:

Cam profile:

 

 

(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:

Cam profile:

 

 

(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:

Cam profile: