Abstract: The concepts of generalized multibody systems and velocity transform matrix and a new form of acceleration transform are presented in the paper. Based on the Lagrange multiplier method, a new method for dynamic analysis of complicated systems is developed, that is, the velocity transform matrix synthesis method for generalized multibody systems. The resulting dynamic equations do not include the Lagrange multipliers and constraint forces. With the aid of the dynamic matrixes of each uncoupled generalized body and the velocity transform matrix for a generalized multibody system, the dynamic equations of the coupled system are obtained by matrix operations. The method is computer-oriented and easy to be coded. An example is provided to illustrate the proposed method.