The paper deals with the problem of motion planning of anthropomorphic mechanical hands avoiding collisions and trying to mimic real human hand postures. The approach uses the concept of “principal motion directions” to reduce the dimension of the search space in order to obtain results with a compromise between motion optimality and planning complexity (time). 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 probabilistic roadmap planner. The approach has been implemented for a four finger anthropomorphic mechanical hand (17 joints with 13 independent degrees of freedom) assembled on an industrial robot (6 independent degrees of freedom), and experimental examples are included to illustrate its validity.