The paper deals with the problem of motion planning of anthropomorphic mechanical hands avoiding collisions. The proposed approach tries to mimic the real human hand motions, but reducing the dimension of the search space in order to obtain results as a compromise between motion optimality and planning complexity (time) by means of the concept of principal motion directions. Basically, the work includes the following phases: capturing the human hand workspace using a sensorized glove and mapping it to the mechanical hand workspace, reducing the space dimension by looking for the most relevant principal motion directions, and planning the hand movements using a sampling-based roadmap planner. The approach has been implemented for a four finger anthropomorphic mechanical hand, and some examples are included to illustrate its validity.