Parametric Equation of sine wave wrapped around a cylinder

Question

Hello i have a 2 axis machine my machine with Z (linear axis) and C (rotation axis) So what i want is an equation for each axis so that they can produce a profile of sine wave around the cylinder with some variables like the (d)diameter of the cylinder ,(n)number of positive half cycles and negative half cycles and (a)the amplitude (i guess it will be a function of d and n)

thanks

Answer 1

I do not understand what you mean by number of sine waves.

For a single sine wave wrapped around a cylinder radius $a$, its amplitude $A$ axis coinciding with cylinder generator we have

$$ (x,y,z)= ( a \cos \theta, a \sin \theta, A \cos \theta)$$

EDIT 1:

$$ \Delta z -A \sin \theta \omega$$

which can be converted to vertical feed rate and center cylinder angular velocity

where $\theta$ is polar angle. It has an ellipse for its boundary obtained by intersection of a slanted plane inclined at $ \tan^{-1}(A/a)$ to plane of circumference.

To pack in more $(=n) $ waves we have

$$ (x,y,z)= ( a \cos \theta, a \sin \theta, A \cos n \theta)$$