#### BACKGROUND:

If the model of the human hand is created with accuracy by respecting the type of motion provided by each articulation and the dimensions of articulated bones, it can function as the real organ providing the same motions. Unfortunately, the human hand is hard to model due to its kinematical chains submitted to motion constraints. On the other hand, if an application does not impose a fine manipulation it is not necessary to create a model as complex as the human hand is. But always the hand model has to perform a certain space of motions in imposed workspace architecture no matter what the practical application does.

#### METHODS:

Based on Denavit-Hartenberg convention, we conceived the kinematical model of the human hand, having in mind the structure and the behavior of the natural model. We obtained the kinematical equations describing the motion of every fingertip with respect to the general coordinate system, placed on the wrist. For every joint variable, a range of motion was established. Dividing these joint variables to an appropriate number of intervals and connecting them, the complex surface bordering the active hand model workspace was obtained.

#### RESULTS:

Using MATLAB 7.0, the complex surface described by fingertips, when hand articulations are all simultaneously moving, was obtained. It can be seen that any point on surface has its own coordinates smaller than the maximum length of the middle finger in static position. Therefore, a sphere having the centre in the origin of the general coordinate system and the radius which equals this length covers the represented complex surface.

#### CONCLUSION:

We propose a human hand model that represents a new solution compared to the existing ones. This model is capable to make special movements like power grip and dexterous manipulations. During them, the fingertips do not exceed the active workspace encapsulated by determined surfaces. The proposed kinematical model can help to choose which model joints could be eliminated in order to preserve only the motions important for a certain application. The study shows that all models, simplified or not, exhibit a pronounced similitude with the real hand motion, validated by the fingertips' computed trajectories. The results were used to design an artificial hand capable to make some of the hand's functions with a reduced set of degrees of freedom.

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