One reason might be that you're training them to do that. I'm not saying you are, but that you need to be aware that you aren't. If your dog whines and you stop what you're doing because of that, then you're training them to do the behavior to stop the cue, just like any other training.
Another issue might be heat build up. You say you're grinding instead of cutting, because the nails are large. Grinders build up quite a bit of heat, quickly. Even it if isn't that hot, grinding is an unpleasant sensation that they're not typically exposed to.
I'd advice two things. One is to use positive conditioning. My dog doesn't like her nails clipped and never will, but she's stopped a lot of the squirming and is much more tolerant since I've started conditioning her to it being a positive situation. I do this by taking a beggin strip and tearing it into many small pieces. I call her over and just give her a few. I ask her to lay down and give a couple more. Then I may grab her foot and play with it a few times, giving a treat every time I let it go. I may tap her nails with the clipper or even move to another foot. If she tries to pull it away, I just hold it. When she relaxes, I keep playing with it, extending the nail by pushing on the pad or just rubbing it. Then I stop and treat.
When I first started, I wouldn't even do all the nails in one go. I might do one or two nails a day, or one foot. Now, I can quickly do all the way around. I just use the grinder to round off her nails. Whether you pick the grinder or the clippers, it's important to do this step, because you're associating a lot of good with a little bad.
When she would fight me about coming downstairs to potty in the morning I realized I was getting frustrated and mad with her ignoring me and pretending she didn't know what I wanted. I thought about it and started calling her down when I had plenty of time. I had to fight with and coax her the first couple of times, but instead of putting her in the cold to potty, I gave her a treat and sent her back up. Pretty soon, she'd run down the stairs, because she associated being called down with a treat. If she had to go out and potty 1 time out of 10, she'd suffer through it. Use the same logic on yours. Make it a positive experience. They may never like it, but they'll fight and avoid it much less.
The second thing I was going to say was already mentioned. Don't feel like you need to do all claws in one session and never have a time constraint. If you have somewhere to be, then you'll hurry and you won't be patient with minor quibbles on their end. You'll be too aggressive and will increase resistance. Work on it when you know you have plenty of time and be patient. Also keep in mind that heat factor of the grinders. I really would suggest clippers if you're going to take off more than a very small amount. I take off large amounts of dead nail with the clippers, because it's super quick and they don't feel it. Then use the grinder in short burst to round it off and take it closer to the quick, so it'll die back.
There are many good resources on the net for helping you clip a dog without hitting the quick. The best method is to take slivers at a time till you hit dead tissue and just see the tip of live tissue. That's as close as you can take it without quicking them.
