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Obliquity effect considered.
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Minimum speed =240 rpm=N1,r=140 mm

Mass of fly ball =m=5 kg/4 kg

mean speed = N1+N22=20(N2N1)

=240+N22=20(N2240)

N2=252.3076 rpm

N2=212.903 rpm

w1=2π×24060=25.132 rad/sec

w2=2π×252.307660=26.4215 rad/sec

=22.295 rad/sec.

90 mm = 0.09 m

Radius of rotation @ N1=r1=110 mm=0.110 m

Sleeve lift =h=50 mm140 mm

Sleeve arm = horizontal arm =Y=100 mm180 mm

Ball arm = vertical arm =X=120 mm1100 mm

h=YX(r2r1) [r2=140 mm]

50=100120 (r2110)

r2=170 mm

Fc1=mr1w21

=5×0.11×25.1322

Fc1=347.389N

Fc1=157.85N

enter image description here

a=rr1

=140  110=30 mm

a=rr1

=150  90=25

{ X1=x2a2=1202302=116.82 mm

=1002252=96.82

Y1=y2h21=1002252=96.82 mm

=802202=77.4596mm }

Mo=0 +

(Mg+S1)2(Y1)Fc1(X1)+mg(a)=0

S12(96.82)347.389(116.82)+5×9.81×0.03

S1=748.29 N=369.29 N

b=r2r

=170  140=30 mm

b=140  115

b=25 mm

X2=x2b2=1202302=116.82 mm

=1002252=96.82 mm

Y2=y2h2=1002252=96.82 mm

=802202=77.4596 mm

Fc2=mr2w2=593.3813 rad/sec

fc2=278.357 rad/sec

Mo=0+

(mg+s2)2(y2)Fc2(X2)mg(b)=0

s22(0.9682)593.3812(116.82)5×9.81×0.030=0

S2=1431.880 N 1454.291 N

721.195 N

s=S2S1h=1454.291748.2950

=14.12 N/mm 8.97

δ=S1S=748.2914.121

δ=52.98mm/42.09

Spring force @ mid position (S):

s=SS1h1

14.12=S748.2925

S=1101.29 N/545.09 N

N=Nmean=N1+N22=240+252.30762=246.15 r.p.m.

=20645.5 rpm.

For alteration of speed.

N1=NmeansfS . . . . . (sleeve moving downward) . . . . . .( S = spring force @ mid-position)

=246.151101.29301101.29

N=2427rpm/203.293rpm.

=246.151101.29+3021101.29

N=249.48 rpm/208.967

Alteration in speed =249.48  242.7

=6.78 rpm . . . . (ANS)

=5.674 rpm.

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