# Sensitivity Analysis of a parallel Robot

• Hi everyone, i need to know how to analyse the sensitivity of each parameter in my parallel robot. What kind of data do i need and how to process this analyse.

• thank you for the reply.
my parallel robot is a delta robot 3RRR, and i need the sensitivity through a regression method to identify the influential parameters.

• You still aren't defining any of those terms. They are not universal.

3RRR?
Sensitivity? To what? Forces? Torques? Amperage? Voltage fluctuations?
Influential parameters? What parameters, influencing what? Position, velocity, acceleration?

after identification of our robot we come up with some parameters ( joints, masse, lange, friction...). after computing these parameters there are still error in our end effector pose. to minimize this error i need the sensitivity analyse to determine which parameters can i neglect in my calculation to become more accurate end pose.

• SkyeFire,

This is what this "robot" looks like. Not industrial uses a breadboard.

## I know a thing or two, because I’ve seen a thing or two. Don't even ask about a third thing. I won't know it.

• All right, now we're getting somewhere.

This appears to be a drawing robot with only 2 Degrees Of Freedom (DOF) in the XY plane (normal convention is to treat the Z+ axis as antiparallel to gravity). It looks like a cross between a Stewart Platform and a SCARA type robot.

I take it your issue has to do with the drawn circles visible in the photo? I'm guessing that those two non-symmetrical circles were drawn in opposite directions, and should have been perfectly atop each other?

When I see a situation like this, the culprit is almost always backlash (or "lost motion" in some parlance). No set of gears, or linkages, can fit perfectly. As such, whenever a driving gear reverses direction, the driven gear almost always undergoes a moment of being stationary while the driving gear is in motion. This "deadband" is the fit tolerance between the teeth of the two gears, and it is never zero. Your hobby servo motors almost certainly have substantial amounts of backlash internally. Also, they are not high-precision components -- I would be unsurprised if their motion was not 100% linear to the input PWM sequence.

But even if the servos were perfect, you then have the linkages. Every hinge between the servo and the pen holder introduces its own backlash, and the effects in a system as complex as this are often multi-axial and very hard to model out.

Look at a similar type of mechanism, used for actual (low-accuracy) CNC work: https://www.maslowcnc.com/. Now, this does not achieve the ~20micron tolernace of a good CNC machine, but (if calibrated properly), it does surprisingly well for such a simple device. This is in large part because the arrangements of the weight keep the chains in constant tension, so that the backlash between the stepper motor gears and the chains is always on one side, even when reversing direction.

With your "Delta" configuration, it's more difficult to control backlash, but one method to try might be to use a light spring or rubber band to put some gentle tension on the pen holder, constant in a single direction. Another simple approach might be to only allow the pen to move in a single pair of directions while drawing (say, X+ and Y+), and only use negative directions for pen-up transfer motions.

A really advanced technique would be to take very accurate measurements of the pen position for a large number of different servo-position combinations (approached from multiple directions, to account for backlash reversals) and built a compensation table that would attempt to null out the errors mathematically. In industrial robots, this is usually pretty expensive, but worth it for certain high-accuracy applications.