Abstract: This paper discusses the kinematics of dextrous robot hands manipulating an object with rolling and con-trolled sliding on one point contact with finger.The contact constraints of fingers and object are analyzed andthe relationships on position.velocity and acceleration between finger-joint motion and object motion and ob-ject motion are formulated.The motion constraints of 3R,4R and 5R fingers are presented.The theory hasbeen validated by velocity simulation and graphical simulations for a 5-4-5 hand.