Can I change the welding rod without turn off the machine?

Yes, you can, Whether it’s stick welding or Tig welding, you won’t have any issue.

Don’t handle Tig wire with your open hands, you should wear protective gear whenever you are in a working setting.
You can be electrocuted while Tig welding if your hand that holds the Tig wire is not gloved in a non-conductive material. It won’t be enough to kill you but you’ll be re-thinking your choices very quickly.

For weld with a stick, as long as there’s no path to ground you aren't in any danger. Most welders have a published OCV rating tells you how much energy is built up in the unit and how long it takes to dissipate when the unit is switched off.
If you are at all in doubt about your safety while doing this stuff, don’t hesitate to turn off in between change outs if that’s what you feel is best. Be aware of the OCV factor, there will still be live voltage built up inside the unit for a time after it’s turned off or plugged into a live socket.

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