On the Synthesis of Cylindrical Linear Rack Mechanisms

Emilia Abadjieva 1 and Valentin Abadjiev 2
1. Faculty of Engineering Science, Akita University, Akita, Japan
2. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Abstract— The science of the gear mechanisms, which is an independent direction of “Applied Mechanics” covers two main scientific directions: theory of gearing and geometric theory of gear transmissions. The main tasks, which are solved by this direction of the science of the gear mechanisms are: development of adequate approaches to the synthesis and related to it generation of the active tooth surfaces of different types of gear mechanisms; choice of rational form of active tooth surfaces; creation of calculating methods for design and elaboration of innovative drives and etc. The current study is dedicated to the synthesis of one less studied class of spatial gear transmissions – cylindrical rack drives. This type of drives serves to transform the rotation of a cylindrical worm into translational displacement of a gear rack. An analytical dependencies, defining the basic geometric characteristics of this type three-link mechanisms, for the cases when the rotating link is a cylindrical worm, which active tooth surfaces are asymmetric cylindrical convolute, Archimedean and involute helicoids, are presented in the study. This motions transformer should be treated as a special case of spatial three-link rack drive, which rotating link is a convolute, Archimedean and involute worm with a constant axial pitch.

Index Terms— rack drive, mathematical modeling, synthesis, cylindrical linear helicoid, action surface, region of mesh

Cite: Emilia Abadjieva and Valentin Abadjiev, "On the Synthesis of Cylindrical Linear Rack Mechanisms," International Journal of Mechanical Engineering and Robotics Research, Vol. 7, No. 5, pp. 544-551, September 2018. DOI: 10.18178/ijmerr.7.5.544-551
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