Hyperboloid drives (spatial skew-axes gears) are used to transform rotation between shafts with non-parallel and non-intersecting axes. In this paper the principles of mathematical modelling of a tooth contact synthesis for this common gearing case are discussed. The presented research shows that synthesis of hyperboloid gear drives can be achieved by application of mathematical model upon a pitch contact point. This approach is applied to the synthesis of spatial gear sets of Spiroid and Helicon types.

Abstract. Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid 1 and Helicon gear drives. The classical gear drives of this type are the Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion possesses threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three types transmissions with face mating gears and a conic pinion are titled Spiroid and all three types transmissions with face mating gears and a cylindrical pinion are titled Helicon.Principles of the mathematical modelling of tooth contact synthesis are discussed in this study. The presented research shows that the synthesis is realized by application of two mathematical models: pitch contact point and mesh region models. Two approaches for synthesis of the gear drives in accordance with Olivier's principles are illustrated. The algorithms and computer programs for optimization synthesis and design of the studied hyperboloid gear drives are presented.

This work is a brief analysis on the application and perspective of using the walking robots in different areas in practice. The most common characteristics of walking four legs robots are presented here. The specific features of the applied actuators in walking mechanisms are also shown in the article. The experience of Institute of Mechanics -BAS is illustrated in creation of Spiroid and Helicon 1 gears and their assembly in actuation of studied robots. Loading on joints reductors of robot legs is modelled, when the geometrical and the walking parameters of the studied robot are preliminary defined. The obtained results are purposed for designing the control of the loading of reductor type Helicon in the legs of the robot, when it is experimentally tested.

The study treats a specific technological approach for the elaboration of small manufacturing series of highly precise hyperboloid gears with small module of the teeth and with not big dimensions of the gear mechanism. It is based on the application of the elaborated by authors mathematical models, algorithms and computer programs for synthesis upon a pitch contact point and upon a mesh region. A special feature of the established approach is the application of 3D software prototyping and 3D printing of the designed transmissions. The presented here models of the transmissions with crossed axes and face mated gears are indented for implementation into the driving of two type robots: bio-robot hand and walking robot with four insect-type legs.

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