Theory of Machine
In a kinematic chain, a quaternary joint is equivalent to

Four binary joints
Two binary joints
Three binary joints
One binary joint

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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

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

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