Is that the rotational motion of crank shaft during the downward movement of piston that leads to the upward movement of piston in an engine?

Yes - as the crank shaft rotates one half of the pistons are moving upward on either the compression stroke or the exhaust stroke, while the other pistons are moving downward on either the combustion stroke (which is where the energy to do all this movement comes from) or the intake stroke.

You were given suitable yes answers to this yesterday. Please keep all your related questions in one thread (one post).