The promising results suggest that such robotic tools may revolutionise tendon injuries' diagnosis.
The "magic angle" effect happens when a tendon is at 55 degrees to a scanner's powerful magnetic field.
While physicians often find it difficult to correctly position a person's limb inside the close confines of an MRI scanner, the new robot speeds up the process.
An air supply from outside the machine drives plastic gears inside the robot, which supports a person's limb on a platform that can move in any direction to put a tendon at the magic angle.
The robot judges its own position, and even uses image processing software to check whether it has reached the right angle.
It can position the Achilles' tendon correctly in just a few minutes, compared with up to two hours by hand.
Constantinos Mavroidis, director of the Biomedical Mechatronics Laboratory at Northeastern University in Boston, Massachusetts, considers this discovery to be quite impressive.
"This is a very efficient solution to a very difficult problem. I believe that this device has great clinical potential," New Scientist magazine quoted him as saying.
A research article in the journal IEEE/ASME Transactions on Mechatronics says that small versions of the robot can position fingers to better reveal their tendons, and that future devices could apply the magic angle to other tissues, such as nerves.