A 6×6 transformation matrix or screw-matrix, and the joint mode vectors in R6
, are applied to derivethe manipulator Jacobian matrix compactly. And the Subsystem Newton-Euler recursive method basedon the aforementioned matrixes and the Graph theory are applied to solve dynamics problems ofmanipulators with loops. The method can be used easily and expansively in Engineering because of itssimplicity, recursive computation and forming state-space dynamic equations automatically. It also can beeasily adjusted to the kinematics and dynamics or complicated multiarm robots. As an example, formingthe dynamics of a five-link manipulator with one loop is presented at last.