The paper presents a new parallel robot with six degrees of freedom and three guiding kinematic chains of the platform. The principal characteristic of the parallel robot is given by the position on the fixed base of all the six linear actuators. The inverse and direct kinematic problem, the workspace generated through a geometrical method, and the relationships for determining the singularities of the new parallel structure are presented. The robot can be used in assembly tasks or as a module for minimally invasive surgical systems.