input Prob 4 V A output Solutionsolution 1here solution to a

(input) Prob 4 V A output)

Solution

solution:

1)here solution to above problem is given as below first all expression and the solution bysame complex algebra method

2)loop closure eqution assuming crank OA,connecting rod AB,and obset horizontal length OC and vertical length CB,angle phi=m,theta=n

OA\'+AB\'=OC\'+CB\'

hence in complex form is written as

R*(e^im)+L*(e^in)=x+D*(e^i90)

hence slider displacement ids given by real art of equation as

x=Rcosm+Lcosn

imginary part is

0=Rsinm+Lsinn-1

2)here on putting value we get that

n=7.18 degree

x=4.834\'\'

3)here above equation on differentiating give velocity of slider

V=R*(e^im)iw2+L*(e^in)iw3-0

real part is

V=-[Rw2sinm+Lw3sinn]

imginary part is

0=Rw2cosm+Lw3cosn

on puttting value in mention problem we get that

w3=-.2182 rad/s

V=-.3909\'\'/s

5)on differentiang above equation we get accelaration of slider

A=-R*(e^im)w2^2+R*i*a2*(e^im)-L*(e^in)w3^2+L*i*a3*(e^in)

here real part and imaginary part are as here due uniform velocity of crank,accelaration of crank is zero,a2=0 rad/s2

A=-R*(cosm)w2^2-L*(cosn)w3^2-L*a3*(sinn)

0=-R*(sinm)w2^2-L*(sinn)w3^2+L*a3*(cosn)

here on puttig value in above expression we get that

a3=.1319 rad/s2

A=-1.1209 \'\'/s2

6)in this way above problem is solve analytically by complex algebra method for expression and value of displacementn,velocity and accelartion of slider is obtained and above problem can easily solve graphically by relative velocity and accelaration method