Grasping robotic hands is classified into three categories based on the obj
ect connectivity. We decompose the space of contact forces into four subspa
ces and develop a method to determine the dimensions of the subspaces with
respect to the connectivity of the grasped object. The relationships we obt
ain reveal the kinematic and static characteristics of three categories of
grasps. It indicates how contact forces can be decomposed corresponding to
each type of grasp. The technique also provides a guideline for determining
the distribution of contact forces on grasped objects. We analyze how powe
r grasps are Identified from the object connectivity and used to synthesize
hand configurations for grasping and manipulation tasks. A physical interp
retation of the subspaces and the determination of their dimensions are ill
ustrated by examples.