# Which of the following equations can be used for harmonic cam profile design?

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Which of the following equations can be used for harmonic cam profile design?
1. y = r(1 - sin 2α)
2. y = r(α - sin α)
3. x = r(α - cos α)
4. y = r(1 - cos α)

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Correct Answer - Option 4 : y = r(1 - cos α)

Explanation:

Harmonic cam profile: Harmonic motion can be generated by an offset (eccentric) circular cam with a radial follower and is therefore a common form to use for a displacement diagram. Cams with this type of transition curve is commonly referred to as harmonic cams.

The equations for harmonic motion are formed from the basic equation

$y = C_0\ +\ C_1\ \cos\ C_2θ = C_0 \left ( 1\ + \ \frac {C_1}{C_0}\cos C_2θ \right )$

Harmonic motion produces a sine velocity curve and a cosine acceleration curve. There is no discontinuity at the inflection point so that θ  is defined by a single equation for all angles between zero and β .

The equations for the rise starting from θ = 0 and ending θ = β  and y= L are

$y = \frac {L}{2} \left ( 1 - \cos \frac {\pi \theta }{\beta } \right )$

Can be rewritten as

y = r (1 - cos α)

Here r = $\frac L 2$$\alpha = \frac {\pi \theta }{\beta }$