How do I put the plastic gear rack back in place, so that the bobbin drive will turn?

If you mean the little bobbin stick, just push it to the back of the machine and this will disengage the wheel, then follow the diagram for your bobbin winding. :-)

It shouldn't be too tight. Clean out and remove the bobbin/bobbin case. Now, try to turn it. Does it turn any better? If it does turn easily without the bobbin case and bobbin installed you know the bobbin case was out of adjustment.
To adjust the bobbin case reinstall the bobbin case. Slightly move the hand wheel back and forth. There should only be slight movement of the bobbin case. The bobbin case is held in place by a small piece of metal next to the bobbin case.on the lower right corner. Just make the adjustment to prevent the case from movement.
The hand wheel can also be prevented from movement due to the interior parts of the machine being filled with dried greese. If you're feel safe about this you can remove the front, back, etc and inspect for buildup. Clean it up with carburetor cleaner and a qtip. Try not to douse the plastic gears with this. Clean it thoroughtly. Put sewing machine oil on all steel against steel movement. Any plastic movement should be done with a non petrolium product like silican spray. You can move the hand wheel a great deal to observe any parts that may have movement probmems.

1. There are gears that drive the hook assembly. Many machines have plastic gears and can be broken or will dry out and break due to age. Yes, the gears can be replaced.
2. The bobbin driver assembly does not suppose to spin! Under the bobbin assembly is the hook (sharp object) that turns.
3. Test the machine to see if it will sew by placing the needle on the far left and then on the far right. Try both to see if it will sew. If it is sewing on one or the other you will need some adjusting from a qualified repairman. The needle just for your information is swinging too far to one side or the other. The other most likely possibility is the timing is off.

Start by trying to turn the wheel with the bobbin and the auto-thread cassette removed. Look inside to see if there is any thread caught anywhere both in the bobbin area and also in the complicated mechanism where the auto-thread cassette fits.

• If it is still stiff, remove the needle plate, which also holds-down the cover over the bobbin carrier. (You may need to use a coin and a pair of pliers to undo the 2 screws as there is very limited vertical clearance at this point)
• Remove the bobbin carrier, noting which way it fits. Thread and fluff can build up in this area.
• Thread might have become wound round under the rotating component into which the bobbin carrier fits.
• Put one drop of oil in the edge of the large screw in the centre of the rotating component and turn the wheel a few times. Put another drop of oil in the same place and continue to turn the wheel.
• Look carefully with a small flashlight into the case and see if there is any fluff or thread bits caught in the feed dogs mechanism.
• Put one drop of oil onto any joint between moving parts that you can see.

Now, if there is no improvement and you cannot see any threads caught, you need to see if there is anything wrapped round the bevel gear drive under the bobbin carrier rotating mechanism.
If you go to "How to fix Brother's CS-8060 bobbin auto winder to work?" thread on this forum there is a description of how to separate the 2 halves of the case. (I apologize for omitting to say about Large +Screw #6, located in the top of the case where the Auto-Thread cassette fits)

• Splitting the case enables you to have a good look around under the mechanisms and check for any thread or fluff. Put one drop of oil on any moving joint.
• Rotate the wheel, being careful to keep your fingers out of the way as you do so. Take careful note of the area below the bobbin mechanism, where there is a bevel gear that turns the drive through 90 degrees.
• There is also an eccentric part that moves the feed dogs mechanism. Check there is nothing clogging-up this bit. You can use Lithium-based grease very sparingly to lube the cams and plastic/nylon components
• Put one drop of oil onto the needle-shaft, above where it slides through the mounting. Turn the wheel a few times and put just one more drop of oil.
• Look at the crank mechanism that drives the needle-shaft and apply one drop of oil on any moving joint or component.
• While you are in this area check that all the bits that move do so freely, especially the little joints of the auto-thread.
• Have a good look around the area of the bobbin winder, up by the wheel. - Has the bobbin winder drive rubber gone gooey? Is there anything caught up there?

Hopefully you may find what is causing the stiffness. It is not really likely that one of the shaft bearings is tight but you can put a little oil each side of the bearing and continue to turn the wheel to see if this frees-up any.
Take care to wipe any excess oil off, particularly where it might get on anything you sew.
Don't get oil on the drive belt and don't blow any fluff up into the motor area or, especially, the speed-sensor disk (which is a black thing with fine slots.
Assemble the components carefully. You might take a few cell-phone pictures to help remember how things go.

I assume you actually mean the metal ring that holds the small round case that the bobbin itself sits in. There are usually two arms that swing in to hold that larger metal ring in place and then there is a plastic and metal piece that sit behind the large metal ring. fit the plastic piece that may look somewhat like a scoop next to the metal piece that usually has the post the the bobbin fits onto and has a quite sharp tooth on it. The metal ring then goes on to hold those two pieces in place and the two arms swing in to hold the metal ring into place. The bobbin or bobbin case now can be put back in. Hint on metal ring placement: they almost always have a notch that goes at the very top where the arm on the bobbin case sits in when it is in place. You may find it easiest to do this with the machine laying on its back so you don't have to have 4 hands to hold everything in place while putting everything back in.
Good luck!

Bent needle, needle inserted wrong can cause problems. On that particular model of brother it uses a plastic rack, or drive assembly to move the sewing hook back and forth. They have a tendency to slip gears, causing the problem you are encountering. Take out the bobbin case and remove the shuttle cover. Put the machine into its back, set at normal center needle position and look to see, by turning the machines handwheel, if the eye of the needle is below or above the hook on the shuttle. If its above the eye....thats the problem.Very, very common on these inexpensive machines.

The plastic bobbin case should sit on top of the raceway, it should slot in quite easily, once the bobbin case is in put the small metal clip at the top over to hold it in place.

When you have that hook drive gear back out turn the wheel until the needlebar is in its highest position. The bar with the teeth that the gear fits onto should be all the way to the right. Now slide the hook driver gear back on. You can lay the hook back in and slowly turn the wheel. Watch that the point of the hook on its upwards stroke is coming slightly above the eye of the needle. When it does this you will be in the correct position to put the screw back on.
Hope this helps. It may take a couple of tries but you will figure it out.

If model 2010, the problem is a part metal- part plastic part attached to the bottom of the bobbin winding lever, the white tear-shaped thing with the arrow on it. If that will turn past the center of the bobbin it's broken inside. to try a do-it-yourself fix, turn upside down, remove 4 screws, including one by the plug (which must be pulled out for safety anyway) remove bottom case. looking at left end of the works, move the bobbin lever and you'll see the broken part move. The plastic part should be broken about half-way down. You can see how the part should push the white plastic bobbin winding shaft up and down when lever moved. the part can be removed by loosening the 2 tiny hexnuts holding it on the metal shaft. you'll need the smallest size allen (hex) wrench there is. NOTE where the part is at bottom of the metal shaft for when you put have to put it back on. be careful to hold the bobbin winding shaft itself in place, but it's easy to see how it goes back in if it pops out. if the break is clean (like my wife's that I just fixed this way yesterday!) you can put a drop or 2 of good crazy glue in the break, making sure lined up on the sides, then clamp in a vise (or hold firmly together with pliers) for at least 10 mins, longer better. wait at least an hour before putting back. putting back on is a little tricky but you move the bobbin lever to left (open) position, make sure it's just on the end of the shaft (shaft barely protruding) and see where the part isn't pushing the bobbin winding shaft. re-tighten with hex wrench then see if the repaired part now pushes the bobbin winding shaft up and down when you move the lever back and forth. Turn back over and move the lever without a bobbin spool- you should see shaft move up in the middle of bobbin case where it will engage the bottom of the bobbin spool where the x is.
Now if part can't be fixed it is available from auth Singer service center in you state but runs $40 or so. they'll try to tell you they have to install it because of special anti-static gloves that wont fry your motherboard on the machine's computer, but the center in Michigan finally said they would mail it to me. hope this helps! funny I just saw this after fixing our machine which hadn't been used for a long time until I decided I might as well look inside if I was going to have to buy her a new machine!!!