Link 4 of the mechanism illustrated in this figure not to sc

Link 4 of the mechanism illustrated in this figure (not to scale) has a angular of 20 rad/s CW. (1) Find the velocity of point C by drawing the velocity polygon (2) Find angular velocity of link 3. Show Intermediate steps to get full credit. Use a scale 1 mm paper represents 100 mm/s (or if you are using an inch ruler: 1 inch on paper represents 2500 The black dot is the origin point of the velocity polygon.

Solution

solution:

1) here angle of link 3 and 4 are not provided hence to calculate them precisely we use complex algebra method and freduenstein equation as follows

loop closure equation is as follows

here loop is O2ABO4

R1+R2+R3+R4=0

equation in complex form as follows

for real part as

r1=100 mm,r2=150mm,r3=r4=250 mm and for right angletriangle ABC

we get Ab=150 mm,AC=300 mm and BC=165.83 mm

for real part

r1cosN1+r2cosN2+r3cosN3+r4cosN4=0

r1sinN1+r2sinN2+r3sinN3+r4sinN4=0

N1=0and N2=105

on solving equation we get relation as

N3=N4+143.33

3) to calculate N4 we use freduenstein equation we have

k1=.666

k2=.4

k3=.4333

here N4=2tan^-1((-b+-(b2-4ac)^.5)/2a)

a=cosN2(1-k2)+k3-k1=-.3879

b=-2sinN2=-1.9318

c=cosN2(1+k2)+k3+k1=.7366

finally we get

N3=182.49

N4=39.16

4) now for given mechanism velocity triangle is given in attached image we get that as follows

Vac=5000mm/s

Vab=4800 mm/s

Vo2a=3200rad/s

Vo4c=4000rad/s

Vac=5900ard/s

Vbc=3400rad/s

here absolute velocity of c

Vo4c=4000 mm/s

5) for angular velocity of point 3 is average of link ab,bc,ac

wab=32rad/s

wbc=20.5rad/s

wac=19.66rad/sw3=(wab+wbc+wac)/3=24.05 rad/s