A robot arm with free joints has some advantages over conventional ones. A light weight and low power consumed arm can be made by a reduction of the number of joint actuators. And this arm can easily overcomes actuator failure due to unexpected accident. In general such underactuated arm does not have controllability because of the lack of joint actuators. The two-link arm with a free joint introduced in this paper is also uncontrollable in the sense of linear system theory. However, the linearized system sometimes can not represent the inherent dynamic behavior of the nonlinear system. In this paper the dynamic characteristics of the two-link arm with a free joint in view of global motion including damping and friction effect of the joints is investigated. In the case of considering only the damping effect, the controllable goal positions are confined to a specific trajectories. But in the case of considering the friction effect, the system can be controlled to arbitrary positions using the friction of the free joint as a holding brake. Also numerical example of position control is presented.