It feels like there were few technological advances during the Middle Ages, but perhaps that's my own 21st-century-centrism. I'd love to know what they technologies they developed in the Middle Ages.
This reply is going to be heavily biased toward textiles, because that's my thing.
The fulling mill was one. It was the first part of fabric production to be automated, and that was at least as early as the 13th century according to "Industrial Milling in the Ancient and Medieval Worlds: A Survey of the Evidence for an Industrial Revolution in Medieval Europe" by Adam Robert Lucas. Here's a video showing one in use
You also have the switch from the warp-weighted loom (stand up the whole time and swing a stick ("weaving sword") overhead to pack the weft into place) to the horizontal loom (like a modern floor loom), where you can sit while you work and have your feet handle the patterning while your arms handle the shuttle, instead of needing your arms to keep changing tasks. Same video as above, but here's the loom. Here's someone weaving on a warp-weighted loom. I don't recall exactly when that change occurred, but Viking cultures would've used warp-weighted looms, while horizontal looms show up in 14th and 15th century illustrations.
Also: the spinning wheel. It arrived in Europe in the 13th century (yay for the silk road! um, the actual one, from history, not the internet thing), and it made spinning go really fast as long as you were willing to stand in one place (well, pace back and forth 5ft or so) for hours on end, and as long as you didn't need the yarn to be the warp (the high-tension threads) on your weaving. Toward the late middle ages / early Renaissance, you get the invention of the spinning wheel flyer, which means you can sit at the wheel instead and use a distaff and short draw spinning style just like you would with a drop spindle. I've heard disagreement over whether it's the change in spinning style or just 100-200 years of "practice" to credit with it, but, in any case, bans on using spinning wheel yarn for warp were lifted eventually. Even if you still had to spin your warp on a drop spindle, speeding up the weft is a handy thing.
And, oh, why not? There's no evidence of wool cards being used in the Viking period, but there are 14th century illuminations showing them, so they must've popped up some time in there too.
Oh, knitting too. Knitting appears in the Middle East first. The earliest example I'm aware of would be 11th century Egyptian. There are several European examples over the next couple hundred years, and it becomes so recognizably domestic that we have 14th and 15th century images of Mary knitting with baby Jesus.
I don't know what cutoff date you're thinking of or whether the 16th century fits what you're looking for, but a machine for knitting stockings was invented during Elizabeth's reign (1589) by William Lee. She famously refused to grant a patent for it, citing the damage it would do to employment of hand knitters. Interestingly, this is fewer than 50 years after knit stockings really begin to replace stockings made by cutting and sewing woven fabric on the bias.
Completely outside my wheelhouse, that video I linked for showing wool weaving and fulling also includes a segment on the blast furnace.