This unsymmetrical curve is composed of the difference between two harmonic motions, one being one-quarter of the amplitude and twice the frequency of the other. It has the advantages of the simple harmonic curve with almost complete elimination of high shock and vibration at the beginning of the stroke .The rate of acceleration change at the beginning of the stroke is small, giving smooth action at that point. However, this slow start requires a larger cam for a minimum cam curvature. The double harmonic curve requires very accurate machining since the errors of cutting its shape (at the start of stroke) usually negate the advantages gained .As the dwell-rise-dwell cam , the limitation of the sudden change in acceleration at the minimum rise point allows only moderate cam speeds . In general, this curve is better applied to dwell-rise-return-dwell cams in which no sudden acceleration for the complete curve.
Characteristics:
The relationship for displacement is
y= h/2[(1-cosφ)-1/4(1-cos2φ)]
= h/2[(1-cosπθ/β)-1/4(1-cos2πθ/β)]
The velocity and acceleration by differentiating are
v=dy/dt=h/2 πω/β(sin πθ/β-1/2sin2 πθ/β)
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