This paper presents a systematic modeling technique for systems of flexible bodies in large global motion. 4 × 4 homogeneous coordinate transformation matrices are used together with the Finite Element Method. By using homogeneous coordinates, derivatives of the transformation matrices can be represented by differential operator matrices. Due to this fact, one can derive the equations of motion in explicit matrix form. In this paper, the derivation of the general linearized as well as the nonlinear equations of motion are presented. Two typical mechanisms are chosen to show the validity of the procedures. Time history analysis and frequency domain analysis have been done using the mechanism models. The modal time integration technique has been applied to show the validity of the linearized equations of motion. The eigenvalues and eigenvectors of the mechanisms are used for the time integration of the linearized equations. For the frequency domain analysis, plots of changes in natural frequencies of the mechanisms are shown. These results show not only the dynamic properties of the structural parts of mechanism, but also those of the rigid body motions of the mechanism.