There are various studies on the structural and functional constructions of hand prostheses inspired by human biomechanics, and there are different kinds of prostheses available on the market. This paper aims to present the relevant stages of designing a hand prosthesis prototype that is innovative due to its mechanical structure and, therefore, the prosthesis fingers’ DOF and mobility. The prosthesis is designed to have independent finger motion with the rotations of each of the three phalanges and, most importantly, rotation for each of the fingers relative to the palm. All these motions are generated and controlled by micromotors, a microcontroller, and sensors. A reverse engineering technique was applied for obtaining the exterior surface dimensions of the prosthesis and this consequently ensures that this prosthesis looks as realistic as possible. Small, light mechanical parts were designed as components of the mechanical system for the motions of finger phalanges and most of them (gears, levers, shells) were made using 3D-printing technologies (digital light processing (DLP) and/or selective laser sintering (SLS)). Aspects of some technical problems which arose during the prototype assembly are also recorded in the paper. Further research development will focus on the tests conducted on the prosthesis and the consequent adjustments of the prototype.