This is really just more of an excuse to post how simple it is to remove an axle using the Axle puller adapter on a slide hammer, but I figured I would make a basic How-To out of it as well.
This is how I go about it, and there may be other ways of doing it so take this How-To on just how I have done it now on 4 different cougars.
Standard Tool Set
FWD Axle Puller Adapter
Large Pulley removal tool (the claw as I like to call it)
Big F#*% Hammer
Tie Rod/Ball Joint Separator (optional in my opinion)
1. Obviously you will need to remove your wheels and jack up the car, and safely secure it on jack stands.
2. Loosen the axle nut, this normally requires a 32mm socket, but I did have an aftermarket set once that used a 30mm socket. You can either spend $5-10 on this socket or get it from the free loaner program at Autozone(or most parts store have a similar program now).
3. Remove your brake caliper and rotor. This may be an optional step, you might be able to do it without removing it, but I like to get it out of the way. If you have serviced these parts and antiseized everything, its to simple bolts to remove and your rotor should slide right off. IIRC the caliper bolts are 14mm. Be sure to tie the caliper out of the way. I like to zip tie it to the springs.
4. Unbolt one end of the swaybar end link. You may need to place a jack under the lower control arm to compress the spring and take the stress off the endlink, it should like out easily.
5. Disconnect the tie rod end from the knuckle. You can use a tie rod end tool/fork, but I find these have a tendency to tear the boot. I will spin the nut so that it sits even with the end of the treads, then smack the nut with the BFH. You want to hit the nut as evenly as possible, and have as many threads on the nut as possible without leaving the threads exposed. This will minimize the possibility of damaging or stretching the threads.
6. Remove the nut and bolt for the ball joint pinch bolt. IIRC both nut and bolt are 18mm.
7. Spraying a little PB Blaster on the ball joint should help it slide out a little easier.
8. Bring your jack back out, and this time jack on either a solid part of the knuckle or dead center on the wheel hub. You only need to compress the spring a couple of inches, maybe a little more for people with the 4 bolt LCA.
9. Bring out the BFH again and smack on the LCA, until the ball joint pops out. If you have the ball joint separator fork it can be helpful here once you get a gap between the LCA, and the knuckle. Again be careful nut to tear the boot on the ball joint
10. Loosen the top strut mount nut in the engine bay, but do not remove it completely.
11. Now take the Claw, and push the axle out of the knuckle.
12. Lastly, use the FWD axle puller adaptor and a slide hammer to pull the axle out of the transmission or half shaft depending on what side of the car you are working one.
Here is the video I took last night with this tool in action. I have popped out the axle using other methods, but they are all a *****. As you can see from the video I was almost able to pop the axle out using one hand and recording the video at the same time. I will never do this job again without this tool.
Installation is basically the reverse of the removal. Here are a few guidelines.
1. Axle some sort of lube to both ends of the axle shaft to help in side in easier, just about anything will do. If you have the splines lined up correctly they should slide in fairly nicely, sometimes requiring a stern push. This is NOT a time for the BFH.
2. Anti-seize all bolts, you will thank yourself later.
3. For most people (2 bolt LCA) getting the ball joint back into the knuckle is pretty simple. Use the handle from your jack, a pipe, etc, and pry down on the LCA. This should get you enough space to get things lined back up properly(a helper is nice here). A little lube, wiggling, and a hammer will help to get it fully seated again. For those with the 4 bolt LCA this a somewhat dangerous and arduous process, but I have yet to find a better method, and a helper is a must. See the 4 bolt LCA does not swing as low as the 2 bolt LCA, so you must compress the spring. I have yet to find a spring compressor that would help in this scenario. You will need to use about a 2 foot 2x4 and your jack to compress the spring. I found the best place to place the 2x4 is on the swaybar endlink bracket on the strut. The fun part is that all of your suspension components are loose you are will need to control the movement of the strut/knuckle while compressing the spring, and then slide the assembly over the ball joint. Oh, and while doing that you will also need to be prying down on the LCA to minimize how high you need to compress the spring. The more you compress the spring the more dangerous all of the forces become when everything slips and comes shooting down, and it most certainly will a couple of times until you figure it all out.
There you go guys/gals a basic how to for replacing you axle. Like I said I originally start this thread just to demo the axle pulling tool, since many people don't know about including Autozone themselves. So, if you want to rent/borrow the tool from them I suggest going in with the part number. If the store you normally go to does not carry the tool (not all of them do), as them to find a store that does. It will save you a lot of difficulties popping them out using any other method.
Edit: I'll fix spelling and get a few more of the socket sizes needed later.