the turning of the cog until engagement involves a cone (like that on the hub bearing) threading onto a vERY coarse thread moving it toward a race on the inside of the hub (think of a rear cup and cone bearing without the ballbearings). when they engage, they lock up and away you go. the distance, and therefore the amount of rotation of the cranks until engagement, is determined by a combination of how coarse the thread is and the distance separating them when fully disengaged and is a intentional byproduct of the design, which for most of them is at least a century old...

BTW, the engagement mechanism is sometimes called a clutch, i think.