here is my damaged Derailleurs

Step one: replace that cable and the cable housing. It is shot, and even a new derailleur will not solve that (and cable and housing is cheap).

Is there a brand name and model on that derailleur? Looks like you are using a long cage now.

Again, read the Park tool site instructions, they are terrific.

Sorry?.

I don't see anything wrong with it other than a frayed cable. What is the actual problem it's having.

While the ghost effect is a pretty cool trick it makes it hard to see any problem.

Just how is it broke? does not shift? does the chain run off the idler pulley?

oh its shimano but don't know the model name.......i think i am using break cables for shifters......i was told that they could work well....

sorry about ghost effect i shot it with my iphone...... the problem is that when i shift from the lower wheel chain fells...maybe tooth are worn out?

i have decided to buy new 105 shimano 5700, both front and rear and 9 speed 12-30 cassette.....problem is that where i am now i know much more then the local bicycle mechanic so fixing is not option...if fix i prefer o it on my own

if the chain is falling (dropping) off the chainwheels (at the crank) it may just be an adjustment issue.

What speed is the cassette? from the photo it looks to be a 7 speed (hard to tell with the ghosting). if you have a 7 speed cassette, then the freehub may not be forward compatible with 9 speed cassettes.

For the model number, if it is Shimano. this will be stamped on the rear of the parallelogram.

For using brake cable as shifter cables, you can't do this, as the nipple on the brake cable won't fit into the shifter; and they are too large a diameter to fit the gear outers.

For the shifting, and the teeth being worn, although it's hard to tell due to the ghosting, they don't look to bad, ths shifting can be fixed by adjusting, see the Park Tools site https://www.parktool.com/blog/repair-...illeur-systems or Shimano Tech Docs https://techdocs.shimano.com/techdocs/index.jsp for how to.

Would suggest initally just replacing the cables, inner & outer, setting up the RD correctly should fix your issues without needing to buy new parts

rd is 9 speed

For what it's worth, I think we're approaching this wrong. the OP has opened 2 threads on the subject and is getting a bunch of opinions piecemeal without getting an overall sense of his problem.

I think it would be best for the OP, if he take a break, and review a number of tutorials about rear derailleur installation (link to over a dozen), so he can see the big picture and narrow the range of his problems (if any besides adjustments). Once he's close and can identify one or two specific remaining issues, then maybe we can help.

good advice...... thank you....i have just one concern that moves me...will my gear take to my trip safely.....even if i fix them? or i have to change them...i checked some tutorials how to install and adjust Dérailleur but i found that these two screws ( that u move Dérailleur left to right are not working properly) so is it worth to fix it?

this is exactly why I suggested you review a few tutorials (not just one) until you have a sense of the basic adjustments and a sense of how derailleurs actually work.

For example the two screws I think you're asking about don't actually move the derailleur, only the cable does that. The two "limit screws" do exactly what their name says. They set the inside and outer limits to it's range of movement.

By way of analogy imagine an elevator. The cable and motor make it go up and down. At the top and bottom of the shaft are switches that cut the power if the elevator gets that far, so it can't crash into the end of the shaft (limit screws) and the control board (levers) control the motor making it stop at each floor, and not between floors.

As I said, put the bike near your computer and watch the tutorials while also looking at your own bike, and eventually the light will go on and the entire picture will come into focus.

https://www.parktool.com/blog/repair-help

the screws i have mentioned is moving derailleur left or right (i mean the lower wheel) it seems there is no straight line between derailleur (low wheel) and cassette (at highest or lowest position) so i though that two little screws could fix my problem but then i have found that i could not move them

i am so jealous of ppl who have brand new bicycles assembled by professionals

Yes, that makes it easier, but even those need work eventually. I've mailed Chain-L to people in Tbilisi, so I know there are some cyclists there, but don't know if there's a shop. You might scout around and see if there's a local racing club (mtb or road) where someone might help you.

Or you might check with some of the hotels that rent bikes, to see who services them, or maybe this guy who rents bikes to tourists can help or refer you to someone.

lol man u r adorable, awesome and cool thank you

Yes.
As I suggested in one of the other threads, new derailleurs may not be needed. Probably an adjustment problem.
avtandil , please take the time to read the Park tool site, AND better describe the problem.

Here is a glossary to help you use the correct terms. There may be a better glossary, I just did a quick search.
https://www.performancebike.com/bikes...1_BikeGlossary

Also, I count 8 cogs on your cassette. Is that correct ? If you have a 9-speed shifter on your handlebars, then you will not get good shifting. A bike with indexed shifters (most modern bikes like yours) needs to have matching/compatible parts. If you have 8 cogs, then you need the same brand shifter with 8 positions (7 "clicks" plus 1 starting position). You also need an 8-speed chain that is the right width for the cassette cogs.
Since 9 and 10 speed systems squeeze more cogs into the same space, they all have different dimensions and all need to work together as designed. They use narrower chains, and closer spaced "clicks" on the shifters.

Once they are adjusted properly, then they should be fine for your trip.
The 2 screws that I THINK you are referring to are called "Limit Screws". They don't "do" anything while riding or shifting. One prevents the derailleur from overshifting the largest cog into the spokes and breaking everything. The other prevents overshifting the derailleur past the small cog into the frame's dropout. Once your bike is set-up correctly, you should never need to adjust the limit screws (unless installing a different wheel or new derailleur)

well thank you all...

lol i just talked to local guy regarding my bike...and he said: ur chain fells off because u shift chain to biggest cog and smallest chain ring.. and on bikes thats not allowed.....
THANKS FOR GLOSSARY-I REALLY NEED IT

AND I HAVE 9 COGS DEFINITELY

Cross Chaining...ie big ring to big ring, or small ring to small ring, causes excessive wear on chain and sprocket teeth...and poor shifting. Been there, Done that! Sounds like your town needs a bike shop! I think we have 6 of them within 2 miles of me! (one just closed, a bit too much competition)

but could it be reason chain to slip of?

No, being in the big chainring and big cog, or small-small can be a bit noisy, it should still work.

What gear are you in when it slips off ? Can you show a picture of it when it has slipped off ? Saying "The chain slipped off" is not enough information.

chain fells of from lower pulley