Interpolation, the meaning of

I've come across two definitions of (Circular) Interpolation in servo systems.

When drawing a circle with the use of two servo axis, Interpolate means:

a: Before any movement of any axis, a tractory/path is calculated for each axis. Then the axis are started at the same time and travel along its own precalculated position/timeslice path.

b: The same calculation is made. The axis are started at the same time but if one of the axis has troubles meating the position/timeslice path, the other axis (both master and/or slave) follows the problems.

In situation a: the result will not be a perfect circle if one axis has problems. In situation b: a perfect circle is always formed.

Does anyone have reference to a white paper describing interpolation, confirming either of the above?

I can't cite any white papers, but B is the definition of interpolation. A is the definition of a coordinated start of two axes.

I thought interpolation of any type is, given known poionts of a system the process can determine all states between them. Extrapolation is, given the known extremes the process determines states beyond them. The accuracy of either depends on the accuracy and quantity of the known points. For circular interpolation it would mean (usually) given center point, radius, start and stop angles, the process can determine all points defined by this.

A 'coordinated move' would apportion the task of traversing from one of these points to the next to two (or possibly more) axes. (It could be possible that the defined circular path would not be in a plane defined by only two axis movements.)

Who cares as long as the path is a circle.

I like the term circular synchronization or coordination

angle = fn(t,frequency,etc)
X(t)= A*sin(angle)+OffsetX
Y(t) =A*cos(angle)+OffsetY

Where are the two points I am interpolating between?
This is a good place for the application of the chain rule ( think calculus ).

I think of circular interpolation as a term for older technology where data is stored in pre-calculated tables.

The system should be designed so neither axis will stall, by the time an error is detect the part may be ruined anyway.

Rockwell define interpolation as definition a: (the old way of thinking )
Apparently also when using CLX to control the new Kinetix Servo.

I was hoping for the more complex definition b: type of control. I mean you would not damage products, just be a little slower. Some watchdog (time or current limit or whatever) could flag a warning.

If definition a: is interpolation, with which word would you describe definition b:?

you can get arrested for interpolation in georgia. and if a barnyard animal is involved, they will throw the book at you!

ejessen said:

If definition a: is interpolation, with which word would you describe definition b:?

Click to expand...

Interpolation with error handling. You seem to want the axes to slow down by themselves when an following error occurs. This will not happen unless there is a supervisor program that will slow down or stop the rate at which the axes index through their tables. So who writes the supervisor program?
You do!

Our controller can automatically stop both axes when an error occurs. If you just want to slow down then the auto-stops must be disabled and a program written that decides how much and how long the axes must slow down.

Stopping on error is easy, but the trajectory isn't maintained and your product "suffer".
Slowing down may be the work around for an interpolation that does not link/lock the drives, but that works for a master/slave system as well (with means of fast communication).

I am really looking for a white paper defining Interpolation in servo systems. www.dictionary.com define it as the mathematical estimate of a value, which I interpretate as defination a: