3. Two sector gears, located at the ends of links 1 and 2, are engaged together and rotate about O1 and
O2, as shown in Figure. If links 1 and 2 are connected to springs shown, find the equivalent torsional
spring stiffness and equivalent mass moment of inertia of the system with reference to θ1. Assume (a)
the mass moment of inertia of link 1 (including the sector gear) about O1 is J1 and that of link 2
(including the sector gear) about O2 is J2 and (b) the angles θ1 and θ2 are small.
RATIO
OF PI
2
Bt
p
VERTICALDISPLACEMENT
B'in'meter
DI
PITCHRADIUS
F Be
OF
4
02
DISPLACEMENT
Oop
tip
It
GEOMETRYRELATION
4201
M
Nz
EQUIVALENT MASS MOMENT OFINERTIA
USING KINETIC ENERGY
Tea
Tea
IT
t 210203
IT
t
sing
a
J t J2
Iz
I
734 12 sink
734 1202
34
02
22 1 8
J
É ph 42
p
SPRINGS
HORIZONTAL
E
4
REQUIRED
are in parallel
kiz
344 ARE IN SERIES
434
kit k
ksly
ks t KA
t
4701
4
112g
sings
4th
V12
xp
rith
sine
rith 0
EQUIVALENTTORSIONALSPRINGSTIFFNESS
USINGPOTENTIALENERGY
21 kt eat
I ke t 214202 t I k izMiz t E Ksa XI
I 1,411
I knot t Ekta E Fitz kitka rith
I
Kat ke E
t
Kitko rith
t
1,3
1
KtEg I ka t ktz F
t
Kitko rith
t
44
4 05
47
11 43
REQUIRED