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 = \(\frac L 2\), \(\alpha = \frac {\pi \theta }{\beta }\)