Yes, several of the Husqvarna machines have this feature. I have an older Designer SE that I bought used and it does this too. Husqvarna and Pfaff machines are almost identical in their features and functions.

my older Husqvarna Quilt Designer has this feature and it is wonderful.

My Brother Innovis 4000D has it, but just got the machine and haven't tried it yet. Just going by info in the book

I have both the Brother Innovis QC 1000 and Husqvarna Designer SE, both have this feature but I prefer to use the Brother machine, which cost much less $$'s to purchase and has not given me any trouble. I only use the SE to embroider but have to watch it as it as it sews, it sometimes likes to take hissy fits halfway through a design! The repair shop can't find out why it does this, so I have a love/hate relationship with it! I have called her Miss Contrary!

The Viking Saphire, and the Babylock Crescendo. Two I know of for sure. Oh, and the Pfaff Creative Sensation.

the new bernina 750 has it.

The brother laura ashley has the pivot function and the AHA feature. Do you not like the brothers because the FMQ nicely

I think my Bernina has this feature. I've never used it.

Baby-lock Symphony and the Husqvarna machines( Diamond, SE and Sapphire) I have those machine and wouldn't buy a machine without that feature. Good for applique curves etc.

My Bernina 820 has this feature &I like it a lot. Good luck in your search !!