Is there any Open source Automation tool for Mobile devices which can be easily automated without any connection to mahine ( with wifi) ?

I'd recommend appium, which runs selenium, which is open source, and in the cloud, no physcial device needed - but you do need to spend a little money.

Monkey Runner ( http://developer.android.com/tools/help/monkeyrunner_concepts.html ) is open source and free but I believe the device needs to be tethered.

You might also want to look into perfecto mobile.

Good luck!