Abstract: This paper intends to extend Lagrangian dynamics for robot mechanisms having open chains without branching to the generalized case of multi-rigidbody systems. A rigidbody connection matrix describing the interconnection structure of multi-rigidbody systems having tree structure is defined. The fundamental Lagrangian dynamical equations, the recursive : dynamical equations and the dynamical equations w i th simpl if ied coefficients for multi-rigidbody systems with tree structure are developed.