Design a displacement profile for the follower fo a singlede

Design a displacement profile for the follower fo a single-dewll cam. the performance speciications are as follows: Machine cycle is 2 seconds, Rise from 0\"to 2: in 60 degrees, fall back to 0\"in 100 degrees, dwell for the remainder of the machine cycle Select your rise and fall functions so that the fundamental law of cam design is satisfied and the accelerations are minimized. Report the equations for follower displacement (s) as a fucntion of the cam angle (theta) fro each of the three cam segments. Plot the svaj diagrams.

Solution

solution;

1)to minimize accelaration constant velocity diagram would be best option but it will induce high forces at starting hence to minimize accelaration it is better to use constant accelaration follower motion for rise as well for fall

2)for drawing displacement diagram we draw rectangle of base of 6 cm(scale 1 s=3 cm) and height 5.08 cm(scale 1 cm=1 cm)

then divide area of triangle for 60 degree (.33 s) and 160 degree(.88 s) and divide this two area in in five equal parteach along x axis and y axis,then we have draw line as in case of accelartion displacement diagram from origin to dividing segement for half part and then from draw line from top side,with the help of spline join intersection points so we get displacement diagram for both rise and fall,remain time it shows zero displacement

4)displacement from diagram for various time period are as follows

t=0,s=0

t=.06 s,s=.4 cm

t=.13 s,s-1.6 cm

t=.2 s,s=3.4 cm

t=.26 s,s=4.6 cm

t=.33s,s=5.08 cm

t=.44 s,s=4.7 cm

t=.55s,s=3.6 cm

t=.66s,s=1.7 cm

t=.77 s,s=.4 cm

t=.88 s,s=0

for remain time s=0 cm

5) velocity diagram would be straight line joining end opposite corner of two recangle divided on displacement diagram,velocity at variou time and crank angle is given by\'

V=2*w*s/angle in radian

w=2*pi/2=pi rad/s

t=0,v=0 cm/s

t=.06 s,v=12 cm/s

t=.13 s,v=24 cm/s

t=.2 s,v=34 cm/s

t=.26 s,v=34.5cm/s

t=.33s,v=30.48 cm/s

t=.44 s,v=21.15 cm/s

t=.55s,v=12.96 cm/s

t=.66s,v=5.1 cm/s

t=.77 s,v=1.028cm/s

t=.88 s,v=0

for remain time v=0 cm

6) accelaration diagram would be horizontal straight line for two recangle divided on displacement diagram as follows

a=4*w^2*s/(angle in radian)^2

for rise

ar=360cm/s2

for fall

a=-291.6 cm/s2