2 The displacement of a flat-face translating follower in a cam-follower mechanism
is as follows:
• 50 mm rise with a simple harmonic motion for a cam rotation of 00
to 1200
• dwell for 300 of cam rotation
• return to the original location with simple harmonic motion
If the minimum allowable radius of cam profile curvature is 60 mm, what is the minimum
required base circle radius? Determine the offset required, if any, for maximum driving effort
eccentricity during the rise to not exceed 25 mm
2 If a translating roller follower is used, instead of a flat-face follower, in the previous problem, determine the minimum prime circle radius and required offset for the pressure
angle to not exceed 250
in magnitude during the complete cycle.
Answers
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Solved problems based on CAM Profiles | Kinematics of Machines Tutorials
March 18, 2013
By admin
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)
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.