I was basically thinking of designing a machine consisting of a nozzle, filling two gels simultaneously into a bottle, such that one of the gels obtains a double helix pattern inside the other gel. I realize the machine will have to move in and out of the bottle, and would therefore require control systems, and so will the system rotating the bottle. So, I basically need to bring about a straight forward vertical movement, as well as a rotatory movement that will give a double helix pattern.
The parametric equations for a helix are
where θ is the angle the point (x,y,z) makes with the x-axis (projected to the xy-plane) and a is a constant. Since a point on the "double helix" has two different z values for a given x, y value, z you cannot expect to write it as a single function by as two distinct functions.
Given we have the equations for the movements, how do we actually implement these equations into a programme in Matlab, to give us the required motion? Any suggestions would be greatly appreciated. Thanks so much for your time.