74 
The N.Z. Journal of Science and Technology. 
[Mar. 
Horizontal component of acceleration of B 
d 
= (v sin 0 ) = v cos 0 
dO v 2 
-j- — — cos 0 . 
dt r 
Vertical component of acceleration of B 
did -rxt \ d (d . A . a [d0\ 2 v 2 . n 
dt\dt J dt\dt ) \dt) r 
Horizontal velocity of A 
= ~ AO = — — ^\/ 1 2 _ r 2 sin 2 0 + r cos 0^ 
= v (sin 0 -f- 
sin 20 
2 Vn 2 — sin 2 0 
Horizontal acceleration of A 
) 
where n = - 
r 
d ( , sm 20 \ 
= r. v sin 0 + 0 —7 - ■ - T - 
dt V Vrc 2 - sin 2 0/ 
sin 20 \ -y 2 ( ^ n 2 cos 20 + sin 4 0 ) 
n 2 - sin 2 0 ) ~ r (C0S ° + (™ 2 - sin 2 0) 3 / 2 I 
or, since n is usually greater than 5 , it is sufficiently accurate to write 
Horizontal acceleration of A 
v 2 ( a cos 20 N 
r \ n 
Considering any transverse section X of rod at a distance x from little 
end A 
Horizontal component of acceleration of X 
= ( cos 0 + 
r 
l — x cos 20 
i n 
Vertical component of acceleration of X 
v 2 x . * 
= —-sm 0. 
r l 
The horizontal component of the acceleration of X is produced by a 
horizontal force at the crank-pin B only, since the guides can exert only 
vertical forces on the crosshead ; while the vertical component is pro¬ 
duced by vertical forces acting both at the crank-pin B and crosshead- 
pin A; hence, if represents the weight of unit length of the rod at 
section X, 
The total horizontal component of disturbing forces at B due to 
acceleration of rod 
f'XXT V 2 ( n . I — X 
/ Wa- - COS 0 4 - — 7 — 
Jo r \ l 
l — x cos 20\ , 
- dx 
n J 
= W — (cos 0 + 
r \ 
cos 20 
v 2 cos 20 
r 
/ 
x 
W X ~dx .( 1 ) 
n / r n 
where W = total weight of rod. 
The total vertical component of disturbing force at B due to accelera¬ 
tion of rod 
WJ ^ ' /l X\ X 7 
W® — sm 0 _ \ - dx 
v 
r 
•i 
l l 
= — sin 0 
r 
x 1 
W® X dx. 
r 
(2). 
