My first thought would be to find a John Deer dealership that sells lawn mowers and phone them for some free advice as they might be in a better place to give you advice.

My thoughts would be that the clutch might have gone pass the point of no return and has broke up and when the engine is running its could be that as a broken clutch could cause the smoke ( and vibration ) if there is loose bits floating around the engine. The vibration could be unrelated to the smoke if the blade spindle has gone.

To many things to guess what it might be.

Sounds bad but where is it smoking? Generally from underneath or from the engine area and installation? or elsewhere like from underneath? Sounds to me like you have run into something in the grass and bent something in the engine like the crankshaft. You hit something with these machines and the force is transferred inside the engine. Alternatively, and I know it sounds like a silly question but did you check the oil levels first? and now? Sorry to say but it is a trip to the nearest dealer unless you know how to pull one of these apart and put it back together again. The pictures you posted do not show anything obviously amiss, bent or broken so it sound like a serious engine problem to me. Sorry!

Guys I found the issue. The PTO clutch broke and was hitting the arm that turns the left tire, which caused the shaking. We replaced the clutch and now its working fine.

Cappy wrote on Aug 10^th, 2013 at 4:07am:

When I was a kid, I had to mow the lawn with a hand pushed mower (like in the image below, but not as snazzy) and he only paid me 20 cents a week pocket money for doing that and other chores!

daveduck wrote on Sep 9^th, 2013 at 9:50pm:

Yep. That was back in the late 60's or early 70's!

I did have other chores that added it up to 20 cents, but there weren't many. I bought lots of lollies with 20 cents. My chores were NEVER a labour of love for me. If their was a way out of them, I found it! Not to matter too much, my little brother was a goody two shoes who would do them if I didn't. Poor kid did a LOT of chores as a kid. Oh... And I would beat him up if he dobbed me in to our parents!