Sounds like the start of shimming or deathwobble, it will get worse over time.

Not sure about the free play in the steering wheel being the cause, might try a tight steer. But definately get your tires balanced and have the jeep alligned. Also check wheel bearings and tierod ends for play.

I assume you have not lifted the CJ3, but deathwobble is a common problem with lifted Jeeps. The slightest play in any part of the entire axle assembly (from wheel bearings to tie rod ends, to pitmanarm) can cause it, usually after hitting a bump, even the smallest bump on a flat road. The bump causes the entire axle to start shacking violently, up to the point your thrown around in your Jeep and usually only a full emergency stop will stop it.

https://www.youtube.com/watch?v=ncZDRStpFms

As you can see it does not matter if you have coilsprings or leafsprings

Most people install a steering damper and it's gone, but this only camouflages the problem, it does not solve the problem and it will return eventually, probably worse.

Besides play in any part, however small, the biggest issue is the caster that changes after lifting a Jeep. The top of the axle tilts forward and it gets a negative caster. You want caster to be at least neutral or best positive. In Jeeps like the TJ you need to install longer lower suspension arms, most people do not and it keeps coming back. If you have negative caster, the front axle basically starts acting like a shopping trolly with one wheel stuck that starts to flutter and you cannot steer until you stop and go again.



Now i'm not to familiar with the Willys yet as in how far the above translates to the Willys deathwobble or shaking symptoms. Mine also has steering wheel play and there is a litlle bit of play on one tierod end but no wobble or shaking at all, not even on uneven or bumpy paved roads. I did have the tires balanced and had it alligned.

So i advice to do that first before you start replacing parts. You can do the alligning yourself with a string.

Just the first hit i got on youtube:

https://www.youtube.com/watch?v=AuYsd7SUwTA

All good points from above.  One other easy thing to check, which also causes this phenomenon, is when the drive shaft is 'out of phase.'  Or bent/damaged.

Here is a link discussing driveshaft phase...

http://www.thecj2apage.com/forums/loud-but-elusive-noise_topic16393_post142906.h...

Start with getting the two truest running wheels up front. If they wobble or the tires are out of true themselves, it will start the wobble. Then try and get rid of where the slack is, like the bellcrank shaft. Then the knuckle bearings as indicated. The steering box itself may have worn sector shaft and bushings. The draglink may also have broken springs inside and is now too loose. Don't waste your money on a steering stabiliser shock. They don't help much. Last is the caster. Sagged springs up front will do this. Sometimes a simple wedge shim will help give you caster. John

If you can feel the shake through the steering wheel then most likely it's in the front end..a knuckle rebuild makes a big improvement..

If it is just a general sort of rumble/shake try the drive lines..check both  front and rear for phase as Tim recommended if you don't have lock-out hubs..

Well, where to start?

Rebuild the steering box, bushings, sector shaft and seal, if you are lucky you won't need a worm shaft.

Rebuild the bellcrank.

Check the pitman arm and bell crank ball ends for wear..if flat on one side or way out of round replace.

Rod end bearings..

check the wheel bearings and seals.

Knuckle bearings too.

I replaced everything in my CJ-5 and STILL the steering was very stiff....but the knuckle rebuild solved all that...

good luck!  Well I can't find an exploded knuckle picture....the Jeep Manual  gives a good explanation though

Austin,
The more modern manuals to suggest the higher pre-loads, but I'm not sure I would set it to 16 lbs.  Your bearings will sound kind of crunchy.

Older manuals had the pre-load specs much lower.  I split the different recommendations and settled on 10-12 lbs. 

Tim

Do you mean the part that bolts on with the four bolts or studs and has the pin? I'm not sure what it is called...

I did not need any for either jeep..all four were fine...get shim packs though...