Project ForgeTheory of Machines
Kinematics of Mechanisms
GATE 2008
Hard
In a cam design, the rise motion is given by simple harmonic motion (SHM) s=(h/2)(1-cos(πθ/β)), where h is total rise, θ is camshaft angle, and β is the total angle of the rise interval. The jerk (d³s/dθ³) is given by
- A(h/2)(1-cos(πθ/β))
- B(π/β)(h/2)sin(πθ/β)
- C(π²/β²)(h/2)cos(πθ/β)
- -(π³/β³)(h/2)sin(πθ/β)
Explanation
Differentiating s three times with respect to θ: ds/dθ=(π/β)(h/2)sin(πθ/β); d²s/dθ²=(π/β)²(h/2)cos(πθ/β); d³s/dθ³=-(π/β)³(h/2)sin(πθ/β)=-(π³h)/(2β³)sin(πθ/β).
Source: GATE ME 2008 (2008)
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