There are two main categories of biking, which are mountain biking and road biking, if you are a mountain biker and you want to use a 10-speed derailleur on a 9-speed cassette then it is not possible ad the setup isn’t compatible with each other, but if you are a road biker then you have a piece of good luck and you can easily use 10-speed derailleur with 9-speed cassette without any difficulty and problem. but if you want to use the Shimano company derailleur then these have different pull ratios and would not be able to use them and interchange them with the 9-speed cassettes, so if you are looking for the 10-speed derailleur buy Campagnolo or SRAM derailleur for compatibility because the pull ratio of these brands is exactly the same and interchangeable with each other.
And also Shimano, SRAM, and Campagnolo brands of derailleurs and shifters are not compatible with each other and you can not mix and replace them with each other. when you try to shift the gears in the cogs of the cassette, the chain would not shift between the cogs, rather the chain will skip from the cassette towards the lowest cog, as a result, the chain will stuck in the cog. to solve this issue you have to tight or lose the limit screws of the derailleur and barrel adjuster of the gear shifters for the proper working of the cable pull and cable pull ratio.
You also have another option, there are small spacers that are inserted in the lower end of the cables where the cables are inserted within the derailleur mounts, and sizes of these spacers are 5mm and 6mm, by inserting these small negligible spacers within the cable gears, you can easily adjust and make the cable pull ratio compatible with the gear shifters and derailleurs. but still, by adding spacers, you would get a better result of the 10-speed derailleur because the shift of gears does not occur properly and the chain moves within the cogs of the cassette very slowly and abnormally due to the different pull ratio of the 10-speed derailleur and 9-speed cassette.
7-speed,8-speed, and 9-speed rear derailleurs and gear shifters have the same pull ratio, and you can easily replace and interchanges these derailleurs and gear shifter with each other but 10-speed derailleurs and gear shifters have different pull ratio, it is the reason that 10-speed derailleurs and gear shifters are non-compatible with the 7,8 and 9-speed derailleurs and cable pull ratios. different value of cable pull ratio means the lining of the derailleur does not stay flat and smooth, but it will constantly move laterally and longitudinally due to different pull ratios of the derailleur and shifter.
The cable pull ratio of the 9-speed cassette works fine with the 10-speed derailleur if you are using just 1 to 7 gears but when you try to shift the gear in the higher 8th cog then you will notice the shifting is not occurring correctly and the chain is again slipping and skipping towards the lower cogs and when you try to shift the gear in the higher 9 cogs of the 9-speed cassette, the chain will not stay in this cog and it will again start shifting towards the lower cogs, so it is the main issue of this setup, and this issue can be solved by adding small sized spacers to make the cable pull ratio and movement of the 10-speed derailleur compatible with the 9-speed cassette.
Chains of 9-speed and 10-speed cassettes have the same compatible width but the right and left sides of the chain plate have different widths for both of them, but these plates would not affect the 10-speed derailleur and the chain will smooth roll through the derailleur, jockey wheels, and derailleur cage.
Chains of 10-speed cassettes have narrow widths and the chains of 9-speed cassettes have wider widths, which means a 9-speed cassette is going to install narrow width of chain, which is also fine for 9-speed cassettes and 10-speed derailleurs.
Using Of Zip ties:
Zip ties are also used for cables, shifter, derailleur, and the derailleur cage to make a 10-speed derailleur compatible with the 9-speed cassette and chain, but the issue is that using zip ties is not a permanent problem solver solution, these are made of plastic and rubber, these will break on the trails when you are shifting the derailleur and side by side moving of the derailleur. and also using zip ties have an advantage, these will make the 10-speed derailleur compatible with the 9-speed cassette.
10-Speed Shimano Derailleur And SRAM 9-Speed Cassette:
Shimano company derailleurs would work accurately with the 9-speed derailleurs by inserting small-sized spacers in the cables of the gear shifters at the rear side of the derailleur. even you can also use 10-speed Shimano derailleurs with 9-speed SRAM gear shifters, you just have to make the cable pull ratio between both of these parts compatible with each other, which needs the insertion of small-sized spacers.
Difference In Cogs And Teeth Of The Cassettes:
The cogs and teeth of the 10-speed cassettes are wider and thicker than 9-speed cassettes, which means thicker teeth cassettes are designed for narrow chains and narrower widths of cogs and teeth of 9-speed cassettes are designed for thicker and wider chains.