We present an algorithm to characterize the space of identifiable inertial parameters in system identification of an articulated robot. The algorithm can be applied to general open-chain kinematic trees ranging from industrial manipulators to legged robots. It is the first solution for this case that is provably correct and does not rely on symbolic techniques. The high-level operation of the algorithm is based on a key observation: Undetectable changes in inertial parameters can be interpreted as sequences of inertial transfers across the joints. Drawing on the exponential parameterization of rigid-body kinematics, undetectable inertial transfers are analyzed in terms of linear observability. This analysis can be applied recursively, and lends an overall complexity of $O(N)$ to characterize parameter identifiability for a system of N bodies. Matlab source code for the new algorithm is provided.
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