I just reviewed the affordance properties that produce the spatial structure in reach-to-grasp actions, and there's an unquestioned assumption lurking in that analysis. Luckily, Mon-Williams & Bingham (2011) actually did question it, so I wanted to cover that part of the paper here.
The assumption in the analyses I described last time is that the unit of action is the aperture between the finger and thumb, and not the fingers themselves. Bingham refers to this as an opposition vector (Iberall, Bingham, & Arbib, 1986; van Bergen et al, 2007). In some ways, this is a weird idea; the action system working to control a space between limbs, and not the limbs! Smeets & Brenner (1999) proposed that grasping is actually about the two limbs. Mon-Williams & Bingham tested these hypotheses and found evidence in favour of the opposition vector.
I want to walk through this in a little detail, though, as of course identifying the relevant elemental variables is part of an UCM analysis, and affordance research helps here too. The task analysis that reveals affordance property options also points to effectivity property options (at least it should - these are complementary after all!). But another part of the UCM approach is that it can, in principle, test hypotheses about elemental and performance variables, so I want to lay this out as well.