Creating cam-profiles

I should want to create a cam-profile where the jerk starts from zero and is smooth all over the profile and ends at 0.
The profile is from dwell to dwell.
Is using a 7th order polynomial at least for start and end of profile the only option for a starting and ending with jerk = 0?
Are polynomials the best way of constructing a cam-profile? What about sine or modified sine curves?

You need to use a quintic or 5th order spline. As far as I know there aren't any motion controllers that do this. I do have all the math worked out but you are the first person that has ever asked for this. If you just want a point to point move there are simpler solutions.
What are you really trying to do?

It really depends on the final motion you are trying to get and whether you are actually going to be machining a cam to make the motion or using a digital controller to generate the cam.

For rotary cams, simple harmonic will give continuous jerk with 0 at the ends of motion. Likewise with modified harmonic motion but in both those cases, the acceleration is non-zero at the end point. If you are using a true rotating cam that never stops, this is probably alright because while non-zero, the acceleration is still continuous if the cam keeps spinning.

Speed plays a big part in this as well. You can get away with a lot more at slow speeds than at high speeds.

Looking in an old textbook (Shigley & Uicker, Theory of Machines and Mechanisms, 1980) I found an interesting reference to an "eighth-order polynomial" cam. The text says it was derived in order to have non-symmetric acceleration characteristics similar to those of modified harmonic motion but with lower peak values of acceleration.

I want to do a point to point move with the maximum possible smoothnes, so I suppose the jerk curve should have no jumps and be smooth.
What I found in literature is that only a 7th order polynomial has no jumps. Lower order can be smooth but I saw at start and end of a point to point move, the jerk goes from zero instantly to a certain value and then follows a smooth profile to end with a instant jump to zero.
I suppose that I will feel the jump to and from zero of the jerk in my machine.

Plc_User said:

I want to do a point to point move

Click to expand...

That is simpler than a cam profile.

What I found in literature is that only a 7th order polynomial has no jumps.

Click to expand...

This is true if you are only going to use one polynomial.

Lower order can be smooth but I saw at start and end of a point to point move, the jerk goes from zero instantly to a certain value and then follows a smooth profile to end with a instant jump to zero.

Click to expand...

It is possible to piece together a few fourth order polynomials. The jerk will change linearly but there should be no jumps if you do it right.

If you want to just use one polynomial to go from start to stop with no constant velocity then 7th order polynomials are the way to go. The peak velocity will be twice the average velocity.

If you are willing to piece together a ramp up, constant velocity and ramp down then you can piece together a few fourth order or fifth order polynomials.
http://www.mate.tue.nl/mate/pdfs/4160.pdf

There are many ways to do this. Some are much easier than others. A simple way of getting a smooth jerk is to use a second order or trapezoidal motion profile but run it through a convolution filter that ramp up and down. This simple to implement but uses a lot of CPU time because of the convolution multiplies. DSPs are good at performing the multiplies and adds.

what platform are you designing for?

If for the control logix 5000 platform there is a combination of AOI's that create the CAM profiles
5,7, modified sine etc
personally I prefer to do it myself (worked out with peters help 2 years ago )