Theory of Machine
The maximum or minimum value of the swaying couple is

± a (1 - c) m.ω².r
± 2a (1 - c) m.ω².r
± c.m.ω².r
± (a/√2) (1 - c) m.ω².r

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Theory of Machine
In the below figure, PC is the connecting rod and OC is the crank making an angle θ with the line of stroke PO and rotates with uniform angular velocity at ω rad/s. The Klien's acceleration diagram for determining the acceleration of the piston P is shown by quadrilateral CQNO, if N coincides with O, then

Acceleration of the piston P is zero and its velocity is maximum
Acceleration and velocity of the piston P is maximum
Acceleration and velocity of the piston P is zero
Acceleration of the piston P is maximum and its velocity is zero

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform pressure, is (where r₁ and r₂ = External and internal radii of collar respectively)

(2/3). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3). μ W (r₁ + r₂)
(1/2). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2). μ W (r₁ + r₂)

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Theory of Machine
The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r cosθ
m.ω².r sinθ
m.ω².r (cos 2θ/n)
m.ω².r (sin 2θ/n)

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