A planar robot for cutting products, such as pieces of meat. The product is displaced along a conveyor or positioned onto a working table and is cut by a tool, preferably a water jet. The tool is held by a pair of arms. The arms have first extremities pivotally mounted on mobile bases. The arms also have second extremities pivotally connected to each other. An actuator displaces each of the mobile bases in order to control the position of the cutting tool in a plane above the conveyor or table.