Theory of Machine
The maximum efficiency of spiral gears is (where θ = Shaft angle, and φ = Friction angle)

cos (θ - φ) + 1/ sin (θ + φ) + 1
sin (θ + φ) + 1/ cos (θ - φ) + 1
cos (θ - φ) + 1/ cos (θ + φ) + 1
cos (θ + φ) + 1/ cos (θ - φ) + 1

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

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