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This is a correction to [Duindam and Stramigioli, “Singularity-free dynamic equations of open-chain mechanisms with general holonomic and nonholonomic joints,” IEEE Trans. Robot., vol. 24, no. 3, pp. 527-526, Jun. 2008] where the singularity-free dynamic equations of mechanical systems with Euclidean or non-Euclidean configuration spaces are presented. We present the correct explicit expressions of the equations presented in the above referenced paper.