The development and diversification of machines and mechanisms with applications in all fields require new scientific researches for the systematization and improvement of existing mechanical systems by creating new mechanisms adapted to modern requirements, which involve increasingly complex topological structures. The modern industry, the practice of designing and building machinery is increasingly based on the results of scientific and applied research. Each industrial achievement has backed theoretical and experimental computer-assisted research, which solves increasingly complex problems with advanced computing programs using an increasingly specialized software. The robotization of technological processes determines and influences the emergence of new industries, applications under special environmental conditions, the approach of new types of technological operations, manipulation of objects in the alien space, teleoperators in the top disciplines like medicine, robots covering a whole field Greater service provision in our modern, computerized society. In this context, the present paper attempts to make a scientific and technical contribution to the kinematic analysis and geometric - kinematic synthesis of gears and gears, both as plane and spatial structures. By definition, these complex mechanisms are composed of bars and lever mechanisms (gears and racks). A remarkable problem with the use of conical gears is the spherical coupling design through three-axis spherical gear mechanisms. This modeling is extremely useful in the construction and kinematics of robots, especially the orientation mechanisms, which explains the particular interest in the use of gears and gears. The cinematic study methods of complex gears with bars and gears are particularly diverse, but a unitary method allows the adaptation and use of more efficient analytical and numerical resolution algorithms. The beginning of the use of gears and gears should be sought in ancient Egypt at least a thousand years before Christ. Here, for the first time, spur gears were used for crop irrigation and worm gears for cotton processing.