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This paper presents a stability analysis of the interaction between a human and a linear moving Force Augmenting Device (FAD). The analysis employs a mathematical model of the human arm, the FAD and their interaction. As a depart from past works, this article presents a stability analysis considering time-delays in the human model. A key ingredient in the analysis is the use of the Rekasius substitution for replacing the time-delay terms. It is proved that the human machine interaction is stable when the human model has no delays. When delays are considered in the human model, the analysis provides an upper bound for the time-delays preserving a stable interaction. Numerical simulations allow to assess the human-FAD interaction. An experiment is performed with a laboratory prototype, where a human operator lifts a load. It is observed that the human machine interaction is stable and the human operator is able to move the load to a desired position by experiencing very little effort. [ABSTRACT FROM AUTHOR]