l Design a doubledwell cam to move a follower from 0 to 2 in

l. Design a double-dwell cam to move a follower from 0 to 2\" in 450, dwell for 1350, fall 2\" in 900, and dwell for the remainder. The total cycle must take 6 second. Use (1) Fifth Order Polynomial (2) Cycloidal Displacement to design the cams.

Solution

solution:

1)here before designing cam we have to draw displacement diagram for cam as per follower motion

2)for fifth order polynomial followr displacement and velocity and accelaration is given as follows

H=2\'\'

m=cam rotation

n=angle for particular ris or fall

S=H(m/n)^3[10-15(m/n)+6(m/n)^2]

V=30h(w/n)(m/n)^2[1-2(m/n)+(m/n)^2]

A=60H(w/n)^2(m/n)[1-3(m/n)+2(m/n)^2]

here for

first rise from 0 to pi/4

we get

S=2(4*m/pi)^3[10-15(4*m/pi)+6(4*m/pi)^2]

for dwell from 45 to 180

s=2

for next fall

180 to 270

S=2-2(2*m/pi)^3[10-15(2*m/pi)+6(2*m/pi)^2]

for 270 to 360

s=0

in the same way by putting value we get velocity and accelaration for cam

4)for cycoidal motion equation are

S=H/pi[pi*m/n-.5sin(2*pi*m/n)]

V=Hw/pi*n[1-cos(2*pi*m/n)]

A=2H*pi*w^2/n^2[sin(2*pi*m/n)]

here displacement for given cycle

for rise from 0 to 45

S=2/pi[4*m-.5sin8m]

for 45 to 180

s=2

for 180 to 270

s=2-(2/pi)[2m-.5sin4m]

for 270 to 360 degree

s=0

in same way by putting angle in radian we get velocity and accelaration by cycloidal motion by direct equation