Abstract: Dexterous robotic hand can stably grasp an object with arbitary shape,and manipulate the object by moving its fingers.The kinematics and force propagation are far more complex than general robotic mechanisms with one open kinematic chain.This paper analyzes four relationships concerning with forces and virtual displace ments between the finger-tips and the gtasped object,the finger-tips and the fingers' joints.Using linear transformation theory,the paper reveals the generant conditions of overconstraint,und erconstraint,and singularity.The grasping effects of redundance,deficiency of freedom,and singular configuration of finger mechanisms are examined.The results developed in the paper can be used for the design of dexterous robotic hand and the planning of the control scheme.