This paper presents some elementary principles regarding constraints on movements, which may be useful in modeling and interpreting motor control strategies for skilled movements. Movements which are optimum with respect to various objectives, or "costs", are analyzed and compared. The specific costs considered are related to movement time, distance, peak velocity, energy, peak acceleration, and rate of change of acceleration (jerk). The velocity patterns for the various minimum cost movements are compared with each other and with some skilled movement patterns. The concept of performance trade-offs between competing objectives is used to interpret the distance-time relationships observed in skilled movements. Examples of arm movements during violin bowing and jaw movements during speech are used to show how skilled movements are influenced by considerations of physical economy, or "ease", of movement. Minimum-cost solutions for the various costs, which include the effect of frictional forces, are given in Appendices.
A hypothesis on the nature of articulatory targets for the vowels /i/ and /a/ is proposed, based on acoustic considerations and vowel articulations. The conjecture is that positioning of points on the tongue surface in a repetition experiment should be most accurate in the direction perpendicular to the vocal-tract midline, at the acoustically critical point of maximal constriction for each vowel. The hypothesis was tested by: examining x-ray microbeam data for three speakers, conducting a partial acoustical analysis, and performing a modeling study. Distributions were plotted of the midsagittal locations of three tongue points at the time of maximal excursion toward the vowel target for numbers of examples of the vowels, embedded in a variety of phonetic contexts. More variation was found along a direction parallel to the vocal tract midline than perpendicular to the midline, supporting the hypothesis. Statistics on formant values for one subject have been calculated, and pairwise regressions of displacement and formant data have been run. An articulatory synthesizer [Rubin et al., J. Acoust. Soc. Am. 70, 321-328 (1981)] has been manipulated through displacements similar to the subject's articulatory variation. Although articulatory synthesis showed systematic relationships between articulatory relationships and formant frequencies, there were no significant correlations between the subject's measured articulatory displacements and his formant data. These additional results raise questions about the methodology and point to the need for additional work for an adequate test of the hypothesis.
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