Transe Axle for Passenger Car

You should take a course in mechanical engineering. That's how complex the "basic design parameters & calculatins for trans-axle" are.

Go down to your local car wrecker/dismantler and spend the day looking at the different setups.

Better still threaten the proprietor with some money and acquire a couple of trans axles for yourself.

Take them home, dismantle them (carefully). Make note of what goes where, attempt to reassemble them.

Take lots of measurements, do drawings, you'll soon get the gist of how simple/complex they are.

At least you'll get an education of sorts and when your done you can recover part of your investment at the scrap merchants..