Accuracy of planar reaching movements. I. Independence of direction and extent variability

This study examined the variability in movement end points in a task in which human subjects reached to targets in different locations on a horizontal surface. The primary purpose was to determine whether patterns in the variable errors would reveal the nature and origin of the coordinate system in which the movements were planned. Six subjects moved a hand-held cursor on a digitizing tablet. Target and cursor positions were displayed on a computer screen, and vision of the hand and arm was blocked. The screen cursor was blanked during movement to prevent visual corrections. The paths of the movements were straight and thus directions were largely specified at the onset of movement. The velocity profiles were bell-shaped, and peak velocities and accelerations were scaled to target distance, implying that movement extent was also programmed in advance of the movement. The spatial distributions of movement end points were elliptical in shape. The major axes of these ellipses were systematically oriented in the direction of hand movement with respect to its initial position. This was true for both fast and slow movements, as well as for pointing movements involving rotations of the wrist joint. Using principal components analysis to compute the axes of these ellipses, we found that the eccentricity of the elliptical dispersions was uniformly greater for small than for large movements: variability along the axis of movement, representing extent variability, increased markedly but nonlinearly with distance. Variability perpendicular to the direction of movement, which results from directional errors, was generally smaller than extent variability, but it increased in proportion to the extent of the movement. Therefore, directional variability, in angular terms, was constant and independent of distance. Because the patterns of variability were similar for both slow and fast movements, as well as for movements involving different joints, we conclude that they result largely from errors in the planning process. We also argue that they cannot be simply explained as consequences of the inertial properties of the limb. Rather they provide evidence for an organizing mechanism that moves the limb along a straight path. We further conclude that reaching movements are planned in a hand-centered coordinate system, with direction and extent of hand movement as the planned parameters. Since the factors which influence directional variability are independent of those that influence extent errors, we propose that these two variables can be separately specified by the brain.