Question

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

Answer 1

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

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