The hand driven drain cleaner from a hardware store will only work effectively over a short distance.
Plumbers have a powered device called an Electric Eel that will cut through almost anything.
This version is similar but smaller. And you can make it.
Step 1: Parts Needed
a length of half inch irrigation piping that is about the same length as the "worm" inside the drain cleaner,
an electric drill, preferably a battery powered on (they have a slower running speed),
a sharp knife, like a box cutter, to cut the above piping to length,
gloves to keep you hands clean and protected from the stuff in the drain..
Step 2: Removing the "worm" From the Cleaner -1
Step 3: Removing the "worm" From the Cleaner -2
Step 4: Pipe Length
Step 5: Insert the Worm
If it becomes too stiff as you proceed shake the piping to free up the worm.
You can pour water into the piping for lubrication. This will make it easier to push the worm through.
The worm must be pushed all of the way through to the end of the piping.
Step 6: Adding the Drill
Step 7: Using the Electric Cleaner
Put on the gloves to protect you hands.
Open up the inspection point of the drain and insert the cutter end of the cleaner into the pipe.
If you have the cutter end slightly bent as shown them it will go around bends in the drain pipe much easier.
It also will cut a wider hole as it goes.
Step 8: Cleaning the Pipe Out
This will be felt as a resistance to the movement in of the piping.
Start up the electric drill.
You will hear a clunking sound as the cutter end rotates and bangs against the side of the drain pipe.
Slowly push the cleaner in.
Listen to the sound of the clunking.
If it slows down too much or stops then back off a little and pull the cleaner back a short distance.
Then slowly push forward again.
You will quickly find out the right amount of push needed on the cleaner to cut through the obstruction.
Step 9: Hints for Use
If the blockage is hard fat then it will work best of you jiggle the cleaner in and out a small amount.
Then slowly push forward, making sure that the clunking sound doesn't stop completely.
If it does the spring inner will wind up and could jam.
The speed of progress through the blockage will depend on how hard the material in the jam is.
I have found that hard fat takes the longest and can be as slow as one tenth of an inch per minute.
Take note of the point where the cleaner first meets the blockage as you will need to cut back and forth several times through that area to completely clear it.
When you have reached the far end of the blockage the cleaner will move forward more freely.
Pull the cleaner slowly back again until you reach the start of the blockage and move forward again.
You can control the length of the cuter end by how much of the spring end is showing at the drill end.
The more showing at the drill end then the smaller will be the hole that the cutter makes in the blockage.
When you have cut through the blockage push the drill forward so the there is no spring showing and pull the piping back through the blockage area to make the largest diameter cut and so clear out all of the blockage.
Step 10: Finishing
It will be dirty with material from the blockage so be careful not to get it on any of your skin.
Pour water down the drain from the sink or shower or bath inlet so that the cleaned and cut rubbish will flow clear down the drain.
Wash down the cleaner and either roll up and store as it is or remove the inner from the piping and push back into the manual cleaner housing.