i have arduino uno R3, i connect it with relay 5v>220v 10A then connect that relay with other one 24V>220V 20A and used other power supply for the second relay 24v AC the first relay 5V have it with drive and everything,transistors and diodes, so i think i dont need to add anything on it the second one without drive just a relay, so my question is: is that ok ?! or i need to add diodes on the second one two i used AC ?! its more easier i think !!
Don't scatter questions about the same project in different parts of the Forum. Many contributors read the different sections so you won't lose by keeping all the stuff for one project in one place.
Keeping all the questions together in the same Thread means that people trying to help have all of the information.
Using one relay to trigger another seems strange - and just introduces more scope for things to go wrong.
The transistor which your Arduino controls can as easily switch a 24v supply for a 24v relay as a 5v supply for a 5v relay (assuming a suitable choice of transistor).
Unless there is some genuine reason to use two relays in sequence don't.
Better yet, use a single solid state relay (SSR). You can easily find an inexpensive SSR for 220 VAC at 20 or 40 amperes, and most can be driven directly from a 5V Arduino output without a series resistor (the relay input is an optocoupler with a built-in resistor).