Theory of Machine
Rectangular bar in a rectangular hole is the following type of pair

Partially constrained motion
Completely constrained motion
Incompletely constrained motion
Freely constrained motion

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Theory of Machine
Lower pairs are those which have

Two elements that permit relative motion
Surface contact between the two elements when in motion
Point or line contact between the two elements when in motion
Elements of pairs not held together mechanically

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

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