93 A cam drive is required for a shaker platform This platfo

9-3. A cam drive is required for a shaker platform. This platform is used to test the shipping-worthiness of packaged items. The cam follower must rise outward 1.0 in. with constant acceleration in 0.7 s, dwell for 0.2 s, fall with constant acceleration in 0.5 s, and then repeat the sequence. Determine the required speed of the cam and graphically plot a follower displace- ment diagram.

Solution

solution:

1)here total cycle time is t=.7+.2+.56=1.4 sec and angle turned is 2*pi

hence required angular velocity

w=angle/time=2*pi/1.4=4.4879 rad/s

2)here equation of motion for constant accelaration are

for process angle turned =m

angle of cam roation=n where 0<n< 2*pi

3)displacemnt ,velocity and accelartion is given by

H=1 \'\', for 0<n<m/2

S=2*H(n/m)^2

V=4*H*w(n/m^2)

a=4*H(w/m)^2

for m/2<n<m

S=H[1-2(1-(n/m))^2]

V=4H(w/m)[1-(n/m)]

a=4*H(w/m)^2

this is equation for rise and fall they avelocity and accelaration relation are same but displacemnt has to subtract from rise present at start of cycle

5)for given operation of cam in given question equation of motion are

for 0<n<pi/2 or 0<t<.7

S=.2026n^2

V=1.818n

a=8.1629 rad/s2

for pi/2<n<pi

S=[1-.2026(pi-n)^2]

V=1.818(pi-n)

a=-8.1629 rad/s2

6) for pi<n<4.039 or for dwell .7<t<.9

s=1\'\'

v=a=0

7)for fall equation of motion are

for 4.039<n<2.2439/2

S=1-.3972n^2

V=3.5653n

a=16 rad/s2

for 2.2439/2<n<2pi

S=1-.3972(2.2439-n)^2

V=3.5653(2.2439-n)

a=-16 rad/s2

7)here using this equation we can easily find displacement ,velocity and accelaration of cam at any instant

here matlab code is

n=[0:.001:pi/2]

S=.2026n^2;

V=1.818n;

a=8.1629;

n=[pi/2:.001:pi]

S=[1-.2026(pi-n)^2];

V=1.818(pi-n);

a=-8.1629;

n=[pi:.001:4.039]

s=1;

v=0;

a=0;

n=[4.039:.001:5.1610]

S=1-.3972n^2;

V=3.5653n;

a=16;

n=[5.1610:.001:2*pi]

S=1-.3972(2.2439-n)^2;

V=3.5653(2.2439-n);

a=-16;

plot(S,n);

title(\'displacement curve\')

plot(V,n);

title(\'velocity curve\')

plot(a,n);

title(\'accelaration curve\')

7)in this way using matlab code we can find displacement,velocity and accelaration curve more easily