Exploratory movements determine cue weighting in haptic length perception of handheld rods

In the present study, we sought to unravel how exploratory movements affect length perception of rods that are held in and wielded by hand. We manipulated the mechanical rod properties--mass (m), first moment of mass distribution (M), major principal moment of inertia (I(1))--individually, allowing us to assess the relative contribution of each of these mechanical variables to the perceptual judgment. Furthermore we developed a method to quantify the force components of the mechanical variables in the total of forces acting at the hand-rod interface, and we calculated each component's relative contribution. The laws of mechanics dictate that these relative force contributions depend on the characteristics of the exploratory movements performed. We found a clear relationship between the relative force contribution of the mechanical variables and their contribution to perceived rod length. This finding is the first quantitative demonstration that exploration style determines how much each mechanical variable influences length perception. Moreover, this finding suggested a cue weighting mechanism in which exploratory movements determine cue reliability (and thus cue weighting). We developed a cue combination model for which we first identified three length cues in the form of ratios between the mechanical variables. Second, we calculated the weights of these cues from the recorded rod movements. The model provided a remarkably good prediction of the experimental data. This strongly suggests that rod length perception by wielding is achieved through a weighted combination of three specific length cues, whereby the weighting depends on the characteristics of the exploratory movements.