Torque/Jerk limited CAM profile

We are trying to develop CAM profiles for a link arm mechanical system that we can set limits on either the jerk of the load or torque of the motor. We currently have a CAM that is optimized for motor torque based off the load inertia but this requires us to run the machine at 100%; which isn't always possible.

Using excel I can get CAMs to work for the accel, but I can't seem to remember how to know when I need to start decel based on position and how long it will take. Can someone point me in the right direction. I recall seeing some equations from Peter Nachtwey years ago; but I can't seem to find them now.

Check this thread
http://www.plctalk.net/qanda/showthread.php?t=38759

tarik did an excellent job of digging up old posts on this topic.

I need to know exactly what the OP is trying to do.

Most of these problems require solving for multiple equations for multiple unknown variables.

tarik, thank you for the link. I searched for hours and couldn't find it.

Peter. The link arm assembly moves a large structure into the machine linearly. The operator can select how far into the machine; so it doesn't actually go the entire 360 degrees that a traditional link/arm system does, but rather 170 degrees of the arm. When we use just a standard linear move on the servo the time for the motion is longer than they want, using the CAM optimized for torque we can significantly reduce the amount of time for the motion. However when they slow down the machine the CAM causes the torque to oscillate since the inertia is lower.

My ultimate goal would be to get the PLC to do the calculations for this and then load the CAM into the servo. I realize the math is much more difficult than PLC traditionally handle so I'd planned to only do a handful of calculations per scan of the PLC and take several seconds to rebuild the CAM.

The tuning needs to change as the inertia changes

The torque is going to be roughly proportional the the angular acceleration.

Basically you want to compress the length of the cam table time wise until the torque or acceleration limits are reached. Since a cubic spline is dependent on all the points there is no quick way to optimize the motion except to use a iterative process. Try reducing the time between all the points until the acceleration limit is reached. Usually there will be one point that is always the limiting point but a better optimizer would try reducing the gap between all points until the acceleration limit is reached but like I said, moving point 3 may affect point 7.

This problem is not trivial. There are optimization or minimization routines that are good for this. They take a little fussing with to get right. Once you figure this out you will see the world in a whole different way.

Look up Nelder-Mead simplex method.
https://en.wikipedia.org/wiki/Nelder–Mead_method

Thanks for the information.

I have only one idea that just might get you by. On our website there is an old program called RMCWin that has a curve tool that is a pretty good cam table editor. You can put in limits for position, velocity and acceleration then move the points until the limits are reached. It is also possible to move the points for multiple axes at a time. This is more of a visual/manual optimization but if you only need to do it once try this.
http://deltamotion.com/files/rmcwininstall.exe
The numbers are all integers and the position extend and retract limits need to be setup before adding points. When done the table can be copied into Excel.

Thanks. I downloaded that months ago when I started working on this; great tool!
This is only a side project of mine so I don't spend a lot of time on it. But recently I had to re-install all of my Siemens software so I took that opportunity to look more into it.