The deterministic parameter identifiability of mechanical linear and nonlinear dynamical systems is considered via linear parameterization of system Lagrangians and necessary and sufficient conditions are established on the identifiability for linear parameters. The identifiability condition results in a new concept, the irreducible Lagrangian representation, and it is introduced to characterize a system Lagrangian with the minimal number of identifiable parameters. A linear parameterization of the Lagrangians for n-degree-of-freedom robot manipulators with rotary joints is presented and, with the help of kinematic analysis, the irreducible representations are further obtained for the PUMA 560 and planar manipulators.

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