A new type of hybrid cubic manipulator with six degree of freedom(DOF) suggested based on traditional serial manipulator and parallel manipulator, three dimensional translation and rotation of output shaft obtained through lineal driving. Define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the fact of mechanism consists of components, a new description method by topological graph theory of components relationship suggested, new description of serial mechanism and parallel mechanism and hybrid mechanism obtained with this method, description elements include component pane and constrained component pane and component relationship line and constrained component relationship line and spacial relative moving capability between adjacent components. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented. Method of analytic geometry used to find the regular cuboid of the reachable working space shape of mechanism, the volume of the reachable working space rest with the limit of translation of couplers, its influential factors obtained, still the rotational angle limits of output shaft at given configuration analysised through the method of drawing, and limit length of guideway etc. are the primary influential factors.