This paper applies the finite twist mapping to spatial manipulators and gives a new approach for the direct synthesis of serial manipulators by using moment invariants and task decomposition. The task is represented in an image space as a cluster of a large number of points and is related to the finite twist of the manipulator. For a given task, the new approach applies a series of analysis to the data, and produces a set of invariant criteria. The type and disposition of the proximal joint are identified, and the remaining regional structure may then be designed. The approach is based upon the numerical analysis of a task without recourse to graphical analysis and is computer programmable. This new design procedure is illustrated with a flowchart and a numerical example is given.