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1 2003

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Construction method of approximated developments of optional length circular arcs

Majewski M.

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

2003

Vol. 13

45--49

This work deals with an analytic-graphical method of construction approximated developments of optional length circular arcs on a straight line. Such problems often appear in the engineering, designing and workshop practices. The method presented by A. Kochański [1] concerns the development of an arc of one-half of a circle, while methods given by S. Polański, A.A. Kowalewski and J. Daniluk [2] as well, as by the author [3] bring approximated results, where the range of measuring errors is 0,1% to 0,6% (for methods included in the work [2]), and 0,0005% to 0,15% (in relation to the work [3]). The solution included in the hitherto elaboration is based on the implementation of a curve - circumference (circular [4]) projection for transformation of final points of given circular arc onto final points of its development on a straight line. The work treats about the geometric idea with it’s justification, which is a base of the (called here) analytic-graphical method. The work presents also a practical part of this method. Presented method gives an accuracy up to 0,052% of length of measured arcs.