Determining joint angles and velocities of a redundant robot system is so far a difficult control issue, especially in attempting to generate natural motions. This paper presents two conventional control methods for a redundant upper limb robot system utilizing the change in manipulability of the finger to execute a task in a free space as well as in a restraint space. In order to clarify and compare characteristics of these algorithms, theoretical analysis and experimental results are demonstrated and evaluated under (1) the viewpoint of giving motion priority to arm or finger, and (2) the calculation viewpoint between a Heuristic Method, which is based on approximate estimation, and a Steepest Decent Method. Two new control methods reducing disadvantages of the above conventional algorithms are also proposed and their utility is verified.