Theory of Machine
In higher pair, the relative motion is

Purely sliding
Combination of sliding and turning
Purely rotary
Purely turning

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

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

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Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

(l₁ + l₂ + l₃)/3
l₁ + l₂ + l₃
l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³

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