For rolling a round or oval bead straight edge or curved edge doesn't matter at all. But when it comes to "S-curves", like on the top of a tear drop shape typical or spinarets (think onion shaped) the curved cutting edge allows you to transition from a roll in one direction to a roll in the other to a straight tapering cut in one continuous move. In the transition you're cutting with the Sweet Area of the skew, with the long point AND heel corner back off the wood. I added an illustration at the bottom of this page to hopefully give you an idea of how such a cut can be made with a curved edge skew. This cut can be done in reverse, starting at the narrow end of the tear drop and pulling back towards the wide part of the tear drop shape.
I practice for more frustrating hours than I care to remember with the straight edged skew. Even a slight lapse in concentration and it was dig in or a nasty spiral cut time. Those pretty much went away once I ground a curve in the cutting edge. Since then I keep finding new, at least to me, cuts I can make fairly easily with the curved edge skew.
While doing these delicate pieces I had NO catches and only two or three spiral cuts, all minor and easily fixed. With a straight cutting edge skew, those spiral cuts would have been a mini-disaster and one would have meant Do Over.
For anyone who has given up on straight edged skews, I strongly recomend trying a curved cutting edge skew and initially skip pine, fir or poplar and go with cherry, or walnut or mahogany.
charlie b
ps - will try doing some illustrations on how to regrind a straight edged skew to make it into a curved edge skew. It can't be done with any griding jig I'm aware of but it really is fairly easy to do free hand - on a sanding disk or the sides of the slow speed, wet TORMEK wheel. DO NOT try grinding with sides of a dry wheel grinder, slow or high speed ( if 1780 rpms can be called "slow" - the TORMEK turns SLOW - as in 50 rpms - and the wheel is THICK - and wet.