The aim of this paper is to present a new six degree-of-freedom (dof) haptic device using two parallel mechanisms. The first one, called orthoglide, provides the translation motions and the second one produces the rotational motions. These two motions are decoupled to simplify the direct and inverse kinematics, as it is needed for real-times control. To reduce the inertial load, the motors are fixed on the base and a transmission with two universal joints is used to transmit the rotational motions from the base to the end-effector. The main feature of the orthoglide and of the agile eye mechanism is the existence of an isotropic configuration. The length of the legs and the range limits of the orthoglide are optimized to have homogeneous performance throughout the Cartesian workspace, which has a nearly cubic workspace. These properties permit to have a high stiffness throughout the workspace and workspace limits that are easily understandable by the user.