Change in effectivity yields recalibration of affordance geometry to preserve functional dynamics

Mon-Williams and Bingham (Exp Brain Res 211(1):145-160, 2011) developed a geometrical affordance model for reaches-to-grasp, and identified a constant scaling relationship, P, between safety margins (SM) and available apertures (SM) that are determined by the sizes of the objects and the individual hands. Bingham et al. (J Exp Psychol Hum Percept Perform 40(4):1542-1550, 2014) extended the model by introducing a dynamical component that scales the geometrical relationship to the stability of the reaching-to-grasp. The goal of the current study was to explore whether and how quickly change in the relevant effectivity (functionally determined hand size = maximum grip) would affect the geometrical and dynamical scaling relationships. The maximum grip of large-handed males was progressively restricted. Participants responded to this restriction by using progressively smaller safety margins, but progressively larger P (= SM/AA) values that preserved an invariant dynamical scaling relationship. The recalibration was relatively fast, occurring over five trials or less, presumably a number required to detect the variability or stability of performance. The results supported the affordance model for reaches-to-grasp in which the invariance is determined by the dynamical component, because it serves the goal of not colliding with the object before successful grasping can be achieved. The findings were also consistent with those of Snapp-Childs and Bingham (Exp Brain Res 198(4):527-533, 2009) who found changes in age-specific geometric scaling for stepping affordances as a function of changes in effectivities over the life span where those changes preserved a dynamic scaling constant similar to that in the current study.