The paper is concerned with description of the mathematical model meant for an analysis of the movement of healds during the weaving cycle. The paper deals with the assessment of the current construction design fastening the heald into the heald shaft. The present condition is characterized by the increased heald loading which is caused by its impact on the supporting wire. As a result of this, the healds get considerably worn out and their service life of the heads is reduced. There is a possibility for passive resistance involvement to reduce the velocity of the heald impact on the supporting wire. In this variant of the solution, the friction between the heald and the supporting wire is used for the decreasing of the impact.
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