In this article, a form of Boltzmann-Hamel equations (Lagrange’s equations in terms of quasi-coordinates), different from the latter’s standard form and avoiding its structurally inherent complexity, is derived based on which a general algorithm for the dynamics modeling of open-chain terrestrial and space robots with an arbitrary number of rigid elements is presented. This form of Boltzmann-Hamel equations is shown to be particularly advantageous in terms of not requiring the determination of the kinetic energy as a function of generalized coordinates and quasi-velocities, representing generalized forces in terms of body basis vectors and offering a panoramic view of the dynamics of the systems. In the act of developing the algorithm, three highly useful kinematic identities are derived via a comparison between the single rigid body equations derived from both the standard and the proposed form of Boltzmann-Hamel equations. These identities are then used to greatly simplify the final dynamics model of both systems. Finally, the equations of motion for a two-link terrestrial robot is derived using the proposed algorithm and simulation results in MATLAB are compared with the model of the system in ADAMS to validate the model.