If the arms AB, CD, be equal, but the describing point P does
not bisect BD, but is brought near to the end D, as in fig. 149, the
regular looped curve will become distorted and will incline towards
C, in the manner shown in the diagram.
Art. 1 10. — Refer now to fig. 150, and suppose the rods to be
moved from the position ABDC into another position KbdC.
Fig. 150.
Fig. 151.
Draw bin, dn perpendicular to AB and CD respectively, and let P
be the point whose position is to be determined.
LetAB = r, bY = x, BM = e,
CD =5, Pd=y, DC</=f



132 Elements of Mechanism.
We shall suppose in what follows that the motion of AB and
CD is restricted within narrow limits, and shall deal approximately
with our equations, by putting

sm - = -, and sm -t =-f ,
22 22

then- = ;^ = =—

_ r (i— cos8)
S (l— cos^)

2 sm'*-
r 2



2 sin^-



= — J nearly.
s <^^

But the link only turns through a very small artgle, which may
be considered to be nothing as a first approximation, in which case
the vertical motion of B is equal to that of D,

.*, bm = dn, or r sin 6 = j sin 0,
whence r d = s <p nearly.
. X r s^ J

y s r' r

b¥ CD
""■p-^^AB'

i.e., the point P divides BD into two parts which are inversely as
the lengths of the nearest radius rods.
