In this paper, the dual area vector of a closed dual spherical curve is kinematically generated and the dual Steineer vector of a motion are extensively studied by the methods of differential geometry. Jacobi's Theorems, known for real curves, are investigated for closed dual curves. The closed trajectory surfaces generated by an oriented line are fixed in a moving rigid body in IR3, in which the closed dual curves from E. Study's transference principle is studied. The integral invariants of these closed ruled surfaces are calculated by means of the area vector. Moreover, some theorems, results and examples are given.