This paper presents a novel six-legged parallel robot, the kinematic model of which is simpler than that of the simplest six-axis serial robot. The new robot is the 6-DOF extension of the Cartesian parallel robot. It consists of three pairs of base-mounted prismatic actuators, the directions in each pair parallel to one of the axes of a Cartesian coordinate system. In each of the six legs, there are also two passive revolute joints, the axes of which are parallel to the direction of the prismatic joint. Finally, each leg is attached to the mobile platform via a spherical joint. The direct kinematics of the novel parallel robot can be solved easily by partitioning the orientation and the position of the mobile platform. There are eight distinct solutions, which can be found directly by solving a linear system and alternating the signs of three radicals. This parallel robot has a large workspace and is suitable for machining or rapid prototyping, as detailed in this paper.