help The delivery truck as shown with the cylinder extending

help

The delivery truck as shown with the cylinder extending at speed 1 ft/min and acceleration 1 ft/min. Draw the mechanism model and the coordinate system. Calculate (1) the initial position of link. AB by specifying the coordinate of point A and B in coordinates, and (2) the velocity and acceleration vector of point B, and the angular velocity and acceleration of link AB and BC.

Solution

solution:

1)here for given mechanism three unknown are present hence we can assume angle of cylinder to be a1=120

2)loop closure equation is

AB+BC+CA=0

hence by complex algebra method

R1cos120+6cosa2+3.1622cos251.56=0

R1sin120+6sina2+3.1622sin251.56=0

on differentiating and assuming cylinder to be fix we get

R1\'cos120=6*w2*sina2

R1\'sin120=-6*w2*cosa2

hence on squaring and divinding we get

w2=.1666 rad/min

as well

tan120=-cota2

a2=-30 or 330

as well initial position

R1=8.39

accelaration of system can be obtain by differentiating

we get

cos120-6*.1666^2cos330-6*A2sin330=0

A2=.2147

2)where velocity of point B is

V=R2*w2=6*.1666=.9996 ft/min

aa=R2*A2=.2147*6=1.2282

3) for intial positon coordinate are assume angle a1=120 and a2=330 and a3=251.56

A(1,0)

B(5.196,-3)

c(0,3)

O(0,0)