Move along between two points

I have a sawblade and I can move it left/right or up/down, but I want to make it move accordingly to an angle. Or rotate the whole system, so it moves like up/down, but because it is rotated it will move diagonally. I believe there are tons of ways implementing this

This code I use for moving, and it works fine.

pos = transform.position;
yNow = transform.position.y;
pos.y = yNow + Time.deltaTime * liftSpeed * direction;
transform.position = pos;  

Then if it hits a specific collider it moves onto another direction.

This is how it looks
I tried to rotate the whole structure like this
but, the blade still goes straight to the top, because it moves as Y being incremented

So basically all I want is to move the blade between those points, but I’m clearly missing something

If you want to move the transform according to it’s rotation, just use it’s own up and right parameters, as they are relative to the transform’s rotation. So, say you want to move your sawblade upwards relative to it’s rotation, you do this:

transform.position += transform.up * Time.deltaTime * liftSpeed;

Hope that helps!