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The content of this monograph covers the following main aspects: (1) New ideas in the field of spatial gear mechanisms, including rack drives, (2) Common kinematic theory of the process of spatial transformation of rotation into rectilinear translation, (3) Mathematical models for geometric synthesis and computer visualization of conic, cylindrical and face helicoids; (4) Mathematical models for synthesis and visualization of three-link rack drives, which rotating links are conic, cylindrical and face helicoids, (5) The achieved results are: analytical and computer synthesis of the linear helicoids of type convolute, Archimedean and involute, (6) Here are also presented analytical and program synthesis of the mesh region and active surfaces of the tooth racks of the corresponding rack drives. This study should help to all who have current interest in the field of mathematical modeling of gear drives.
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