This paper discusses general algorithms of some ruled surfaces elements development. Analytical algorithms of curves belonging to developable surfaces development are described. Surface elements developments are made by geometric problems solving in vector and matrix form. Algorithms for curve belonging to the conical surface with the apex position known and for curve belonging for cylindrical surface with ruling direction known are presented. The tangent developable surface edge of regression development algorithm is also considers. Proposed algorithms can be imported into existing computer mathematical and graphics software with appropriate macros. We formulated and proved the theorem about invariant rotation method of three-dimensional Euclidean space around to the axis of an arbitrary direction and passing through an arbitrary point of the space. General differential equation was obtained to describe kinematics of space curve bending in the process of surface development. The proposed algorithm is illustrated by example of circle on cylinder development.
|投稿的翻译标题||MATHEMATICAL ALGORITHMS FOR DEVELOPABLE SPACE THIN-WALLED STRUCTURES PATTERN CUTTING|
|州||Published - 2017|
Level of Research Output
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