I think you might be talking about the elbow coming out of the bottom of the throttle housing. If the bike is 1996 or later, they are held in place by a small compression ring, and to take them out you have to pull and twist while pulling. a little wd 40 will help. they can be a real pain to disconnect. As another stated, they are sized differently so they cannot be put on wrong. Be sure you loosen the throttle cables and take them out of the throttle sleeve before pulling the elbow loose.
For 1995 and older bikes, the elbows are threaded and a small 7/16 or 3/8 wrench is all thats needed to release them.
Place a 5/32-inch thick piece of cardboard, about 1" by 1", between the brake lever and the lever bracket.
Loosen the cable adjuster jam nuts with the appropriate-sized Torx driver head. Screw in the cable adjusters with the screwdriver until they are as short as possible.
Use a T-25 Torx drive head to remove the right upper and lower switch housing screws.
Loosen the upper screw securing the handlebar clamp to the master cylinder housing with a T-27 Torx drive head.
Remove the lower clamp screw and the flat washer.
Detach the brass ferrules from the notches on the inboard side of the throttle control grip then remove the ferrules from the cable end fittings.
Pull out the crimped inserts at the bent tube end of the throttle and idle control cables from the lower switch housing.
Remove the air cleaner from the bike by unscrewing the three screws that attach it to the bike. Remove the back plate by unscrewing its three bolts and one Torx head screw.
Detach the cables at the carburetor. Use the slots on a pair of wire cutters to remove the cable barrel ends from the holes in the throttle wheel and release the cable housings from the cable guides on the carburetor cable bracket.
Use the wire cutters to cut off the 1/4-inch cable straps securing the cables to the frame's backbone and coil bracket. Then remove the cables.
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One throttle cable pulls the throttle cable bracket to provide acceleration, while the other cable helps to push the bracket back into place. Harley recommends replacing both of these cables should one of them become broken or excessively worn.
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