Open problem: accuracies on parallel robots

Several roboticians do advocate that parallel manipulators offer better accuracies or precision.
I have read it so many times in so many papers.
But, I never saw yet neither the proof or the experience of that.

In theory, this should be the case since the errors could average out in terms of position accuracies.
However, my experience on the Mikron Triaglide, Demaurex Delta (EPFL), Hexaglide (ETHZ), Hexapod (CMW), etc and in my simulation trials, in certain instances, these errors could almost cancel. On the other hand, on these cases, orientation errors did add. Hence, the resulting milling surface finish was of very poor quality. Even with very good calibration techniques, the Triaglide could only achieve milling on a very small portion (5%) of its workspace. This issue is even more critical on Delta robots where the rotation errors could not be compensated even by the finest actuated moves.

Therefore, the best results that were obtained could only insure roughing at somewhat slow feedrates. These would not be better than classical Cartesian machines. Of course, the parallel robots could be made to run with faster accelerations in the case where linear axes are not applied, but this would continue to also result in worst accuracies.

I am still questionning if anyone could design a parallel robot which showed that they can be more precise than a Cartesian milling machine. I would make this an open problem.

Luc