Control of underactuated manipulators is an attractive research theme in robotics. One of the reasons is that they become a complex system, so that they cannot be controlled by normal any control methods. These systems also include the properties of nonholonomic systems. One of control methods used for underactuated manipulators is known as a switching control, which selects a stable controller out of ones prepared in advance by using a switching rule. In this paper, we propose a switching control method for three-DOF underactuated manipulators. The dynamical model of an underactuated manipulator consisting of two prismatic joints and one revolute joint is first transformed into an extended nonholonomic double integrator form. Such a system can be controlled by applying the conventional logic-based control method developed in the case of velocity constraint, after slightly extending it to the present case. The effectiveness of the proposed method is illustrated through simulations with a three-DOF underactuated manipulator.