A method to calculate degrees of freedom (mobility) of parallel manipulators has recently been suggested by Gogu. The method is based on linear algebra, and structural parameters utilized in this method include connectivity, redundancy, and overconstraint. In this thesis the author deals with situations of multi-fingered grasping of an object. Fingers and objects are considered as the limbs and the moving platform of a parallel manipulator, respectively. The degree of freedom is calculated by using the method suggested by Gogu. As the grasping is firm, a finger is considers as a part of the object. If relative slip occurs, then the finger is considered to be connected to the body by a planar pair. Degrees of freedom are calculated for several types of mechanical fingers, and with various numbers of slipped fingers. Comparisons to the popular CGK formula are also given in this thesis.