How do I move stacked cubes in a dynamic way?

I'm making a game similar to Pancake Run, that I collect and stack objects along the way. However, my stack moves absolutely stiff. I tried using different joint types but couldn't achieve the "almost toppled" effect. For example, when I move to left, I want my cubes to swing as if they are connected. I tried using a loop to iterate through all the objects in the stack and registering the horizotnal movement from bottom to top, but since they are childs of the same parent, it didn't work. So what kind of an approach should I follow?