Language and action have been found to share a common neural basis and in particular a common 'syntax', an analogous hierarchical and compositional organization. While language structure analysis has led to the formulation of different grammatical formalisms and associated discriminative or generative computational models, the structure of action is still elusive and so are the related computational models. However, structuring action has important implications on action learning and generalization, in both human cognition research and computation. In this study, we present a biologically inspired generative grammar of action, which employs the structure-building operations and principles of Chomsky's Minimalist Programme as a reference model. In this grammar, action terminals combine hierarchically into temporal sequences of actions of increasing complexity; the actions are bound with the involved tools and affected objects and are governed by certain goals. We show, how the tool role and the affected-object role of an entity within an action drives the derivation of the action syntax in this grammar and controls recursion, merge and move, the latter being mechanisms that manifest themselves not only in human language, but in human action too.