This paper addresses the problem of grasp synthesis with force-closure for 3D articulated objects consisting of n links and considering frictional and non-frictional contacts. The surface of each link is represented by a finite set of points. First, the article presents a methodology to represent the generalized wrench space for an articulated 3D object with n links. This wrench space is generated by the forces applied on the links of the articulated object. Second, the algorithm that finds the set of points which allow a force-closure grasp using the generalized wrench space is described. The approach has been implemented and some illustrative examples are included in the paper.