# What does the following expression represent with respect to a spline cam? $\ddot{\overline{u_4}}=\ddot{\overline{u_5}}=\frac{\ddot u(\theta_B-\theta 0 votes 30 views in General closed What does the following expression represent with respect to a spline cam? \(\ddot{\overline{u_4}}=\ddot{\overline{u_5}}=\frac{\ddot u(\theta_B-\theta_c)^2}{4L}$

1. Normalised acceleration on the return part
2. Normalised acceleration on the rise part
3. Normalised velocity on the return part
4. Normalised velocity on the rise part

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Correct Answer - Option 1 : Normalised acceleration on the return part

Explanation:

Spline Cam: The spline method of designing cams is based on using cubic polynomials to fit a given displacement diagram at a predetermined number of points. This method is used for designing nonstandard cams.

The normalized velocities and accelerations for a spline cam are, respectively, as follows

On the rise part:

Velocity

$\dot {\bar u_1} = \dot {\bar u_2} = \frac {\dot {u}\theta_A}{2L}$

Acceleration

$\ddot {\bar u_1} = \ddot {\bar u_2} = \frac {\ddot {u}\theta_A ^2}{4L}$

On the return part:

Velocity

$\dot {\bar u_4} = \dot {\bar u_5} = \frac {\dot {u}(\theta_B - \theta _C)}{2L}$

Acceleration

$\ddot {\bar u_4} = \ddot {\bar u_5} = \frac {\ddot {u}(\theta_B - \theta _C)^2 }{4L}$