If your drain snake won't make a turn, it could be for a number of reasons. One possibility is that you're using a snake that is too hefty for the job. Another possibility is that it's catching on a snag caused by pipe corrosion. A third scenario could be that it's contacting the clog at the point at which you think it should be turning a corner. If your snake is too big for the job, try a smaller one. If it has hit a clog, now is the time to crank it.
Choose the Right Snake
Just as plumbing pipes come in various lengths and diameters, drain augers come in various sizes to match them. The largest is a sewer auger, which can be 1/2 inch in diameter or more and up to 50 feet or more in length. If you try to use one of these on your toilet, the snake won't go down the toilet, nor will it make it past the first bend in a sink P-trap, and it will probably cause some damage.
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Toilet augers, as described by the website Home Gear Kit, are typically 3/8 inches in diameter and from 3 to 6 feet in length. They are designed to wend their way through the internal trap of the toilet as far as the waste opening and maybe a little farther.
Sink augers are designed for 1 1/4-inch and 1 1/2-inch sink pipes. The typical diameter is 1/4 inch and they are usually longer than toilet augers. Sometimes they are wound into a coil in a plastic drum with a handle.
Drain Snake Won't Make Turn
The proper way to use a snake is to insert the head into the drain and push very slowly without cranking. If you try to force it, it can bend back on itself and actually come out of the drain. Push gently and slowly, and if the auger is the right one for the job, it should slide smoothly through the pipe.
When you can't push the snake any farther, that usually means that it has hit the obstruction and it's time to crank slowly to work the head through the gunk. When you do this, material will collect on the head, so you have to pull the snake out periodically to clean it. If you pull it out and there's nothing on the head, it could be because the clog is composed of a material the head can't penetrate.
If you suspect the snake is getting stuck in a corner, try operating the crank in reverse. This makes the head wobble back and forth, but because you're cranking counterclockwise, it can't collect any debris. If the bend in the pipe is really at fault, the wobbling of the head should help the snake clear the corner. If there's an obstruction, the snake will still get stuck.
Snake Can't Unclog Kitchen Sink
You can't always clear a sink clog with a snake. Some clogs are caused by materials that become too hard in the drain for the snake to penetrate. When a snake doesn't work, plunging probably won't either, so the best strategy is to disconnect the P-trap and clean it.
While you have the trap off, it's a good idea to insert the auger directly in the waste line, just in case the clogs happen to be there. The snake might not have been able to reach the clog from the sink opening, but now it might be able to.