The actualization of action possibilities (i.e., affordances) can often be accomplished in numerous ways. For instance, an individual could walk over to a rubbish bin to drop an item in or throw the piece of rubbish into the bin from some distance away. The aim of the current study was to investigate the action dynamics that emerge from such under-constrained task or action spaces using an object transportation task. Participants were instructed to transport balls between a starting location and a large wooden box located 9 meters away. The temporal interval between the sequential presentation of balls was manipulated as a control parameter and was expected to influence the distance participants moved prior to throwing or dropping the ball into the target box. A two-parameter state space derived from the Cusp Catastrophe Model was employed to illustrate how behavioral variability emerged as a consequence of the under-constrained task context. Two follow-up experiments demonstrated direct correspondence between model predictions and observed action dynamics as a function of increasing task constraints. Implications for modelling, the theory of affordances, and empirical studies more generally are discussed.