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Theory of Machine

Theory of Machine
A pantograph is a mechanism with

Turning pairs
Lower pairs
Rolling pairs
Higher pairs

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Theory of Machine
The equation of motion for a single degree of freedom system with viscous damping is 4(dx²/dt²) + 9(dx/dt) + 16x. The damping ratio of the system is

9/128
44082
30195
44090

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Theory of Machine
According to Kennedy's theorem, if three bodies have plane motions, their instantaneous centers lie on A. A triangle

A straight line
Two lines
A point
A triangle

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

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Theory of Machine
The driving and driven shafts connected by a Hooke's joint will have equal speeds, if

cosθ = sinα
tanθ = ± cosα
sinθ = ± tanα
cotθ = cosα

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Theory of Machine
A machine mounted on a single coil spring has a period of free vibration of tp . If the spring is cut into four equal parts and placed in parallel and the machine is mounted on them, then the period of free vibration of the new system will become

tp /4
4 tp
16 tp
tp /16

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