What is the name of the glucose testing machine that can measure the sugar without pricking the finger?

Many. I think you are talking about alternative site testing. You still have to "prick" something, just not the finger. Some of these sites are: forearm, palm, upper arms, thighs...Most meters now offer alternative site testing:some examples: freestyle, precisionxtra, breeze2, contour, one touch ultra/smart/mini, accucheck aviva/compact plus, true track smart/sidekick.