This work presents a study on the development of an underactuated robot hand. The hand consists of three fingers operated by a single actuator through a triangular joint that provides approximately equal grasp force and compliance among them. A displacement-force conversion mechanism with the spring and feed drive was developed to actuate the fingers. With this mechanism the grasp force can be controlled easily based on the rotary displacement of the actuator. A mathematical model of the contact force was presented and verified by measurement of the fingertip force. The grasp compliance was validated by tests with a variety of objects.