What is the proper way to hold hand grips?

All the pictures I have seen shows that the springs are suppose to be pointing up. But I think it makes more sense to have the springs pointing down. Because the thumbs would then be on the end of the grip, which would work the thumb muscles more.

Hi Anticuchos,
Typically they are held with the springs pointing up, though I think this is more solely for ergonomic reasons. The hand conforms more naturally to the grip in this way. I think you are correct that pointing the spring down will work the thumb much harder. In fact, the thumb will likely do the majority of the work. There is probably no harm in doing this, as long as you are careful not to strain any tendons, as this will give you a very wide grip between the thumb and index finger. Like using an over or underhand grip in many strength exercises, varying such can probably serve to work different groups of muscles.
Hope this helps a bit. Take care.