ON THE SYNTHESIS OF SPATIAL RACK MECHANISMS

Abstract cze:
Abstrakt: Two relatively independent areas of the gearing science have been distinctively outlined and considerably progressed in the last decade. The "Theory of gearing" could be considered essentially as a kinematic theory of mechanisms for motion transformation with high kinematic joints by a defined law. This theory treats the common regularity and research methods of gear sets. The area "Geometrical theory of gears" observes the mathematical modelling of the concrete gear sets. This area also develops the methods for synthesis and generation of the active tooth surfaces. This study belongs to the second area of gear theory. It is dedicated to the analytical defining of conjugate tooth surfaces of a class of the spatial gear mechanisms, called spatial rack sets. They are designed to transform rotation into translation motion by a defined law. The rotation is realized by gear with helical teeth. In the most common case this gear has a conic form. And the translation is realized by rack with helical teeth. In this study the active tooth surfaces of the first link are linear conic helicoid, and the teeth surfaces of the rack are kinematically conjugate of the conic helicoid. The obtained equations are the basis for creation of the algorithms for synthesis and design of the spatial rack mechanisms.

Abstract eng:
Abstract: Two relatively independent areas of the gearing science have been distinctively outlined and considerably progressed in the last decade. The "Theory of gearing" could be considered essentially as a kinematic theory of mechanisms for motion transformation with high kinematic joints by a defined law. This theory treats the common regularity and research methods of gear sets. The area "Geometrical theory of gears" observes the mathematical modelling of the concrete gear sets. This area also develops the methods for synthesis and generation of the active tooth surfaces. This study belongs to the second area of gear theory. It is dedicated to the analytical defining of conjugate tooth surfaces of a class of the spatial gear mechanisms, called spatial rack sets. They are designed to transform rotation into translation motion by a defined law. The rotation is realized by gear with helical teeth. In the most common case this gear has a conic form. And the translation is realized by rack with helical teeth. In this study the active tooth surfaces of the first link are linear conic helicoid, and the teeth surfaces of the rack are kinematically conjugate of the conic helicoid. The obtained equations are the basis for creation of the algorithms for synthesis and design of the spatial rack mechanisms.

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