Engineering Mechanics

Chapter 33 : Transmission of Power by Belts and Ropes „„„„„ 677

We know that the length of the belt,
L= Length of arc GJE + EF + Length of arc FKH + HG
= 2 (Length of arc JE + EF + Length of arc FK)
Substituting the values of length of arc JE from equation (ii), length of arc FK from equation
(iii) and EF from equation (iv) in this equation,

L=

2

12

12

(– )

2– –

222

rr

rl r

l

⎡⎤⎛⎞ππ⎛⎞

⎢⎥⎜⎟+α + + ⎜⎟α

⎣⎦⎝⎠ ⎝⎠

=

2

12

11 2 2

(– )

2– –

222

rr

rrl r r

l

⎡⎤ππ

⎢⎥+α+ + α

⎣⎦

=

2

12

12 12

(– )

2( ) (–) –

22

rr

rr rr l

l

⎡⎤π

⎢⎥++α +

⎣⎦

=

2

12

12 12

(– )

()2(–)2–

rr

rr rr l

l

π+ +α +

Substituting the value of 12

(– )rr

l

α= from equation (i),

L=

2

12 12

12 12

(– ) (– )

()2 (–)2–

rr rr

rr rr l

ll

π+ +× +

=

22

12 12

12

2( – ) ( – )

() 2–

rr rr

rr l

ll

π+ + +

=

2

12

12

(– )

()2

rr

rr l

l

π +++

33.12.LENGTH OF A CROSS-BELT DRIVE

Fig. 33.7. Length of a cross belt drive.

In this case, both the pulleys rotate in the opposite directions as shown in Fig. 33·7.

Let O 1 and O 2 = Centre of the two pulleys,

r 1 and r 2 = Radii of the larger and smaller pulleys,

l= Distance between O 1 and O 2.