Boundary Conditions in Human Movement III: Fourier Analysis of Reaching

C.M. Harris (UK) and M.R. Harwood (USA)

Keywords

: Arm movements, eye movements, minimum jerk, Fourier analysis, measurement noise, boundary conditions

Abstract

We examine empirically the boundary conditions for point to point reaching movements using Fourier analysis. Subjects made horizontal finger pointing movements of various amplitudes without the finger touching the work surface. This avoided low-order physical discontinuities at the onset and offset of the movement, and allowed us to examine the underlying neuromuscular discontinuities. Finger position was recorded at 400Hz with a resolution of 0.1 mm. In the temporal domain velocity profiles were bell-shaped and approximately symmetrical with no abrupt onset or offset. Fourier transforms revealed minima at 1.61, 1.38, 1.52 times reciprocal duration, which are not consistent with the minimum jerk profile (1.84). High frequency slopes of the energy maxima were -6.92, -7.00, -7.28, which is also not minimum jerk (-8). This slope indicates a remarkably low order of discontinuity consistent with an effectively 3 order system. These spectral measurements are remarkably similar to those measured from saccadic eye movements indicating similar shaped trajectories, and are consistent with the minimum variance model with a suitably low order plant.

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