This article deals with the minimal parameters of a manipulator in the least squares sense, so that the minimal parameters are equivalent to the identifiable parameters. The least squares concept is used to introduce terminology for the minimal linear combinations (MLCs) of the system parameters that define a set of linear combinations of the system parameters. The number of elements of the set is minimal, yet the set still completely determines the system. Furthermore, it is shown that the problem of finding a set of MLCs of a manipulator can be simplified to that of finding two individual sets of MLCs that determine the entries of the inertia matrix and the gravity load. Although the approach is applied to the inertia constants of composite bodies to obtain a set of MLCs identical to an earlier one, the result is newly interpreted in the least squares sense. The approach itself is a new method for finding the identifiable parameters of a manipulator, and it yields some new insight into the manipulator dynamics. The crucial feature is that a set of MLCs found by using the present approach is guaranteed to be identifiable. The earlier approaches always require an identification method to verify the results. An equivalence theorem is also presented that rigorously states the equivalence between the different sets of minimal parameters. © 1994 John Wiley & Sons, Inc.