This book comprehensively reflects the summary of theoretical and experimental studies whose conclusions are effective for optimized structural synthesis in precision elasticity, as well as demonstrates a large experience and options in the synthesis and application of precision elastic guides, mechanisms, correctors, transducers, elastic helicoids, and sensors in instruments and machines including their miniaturization for atomic force microscopy and other advanced solutions. The main focus of this book is in the possible simplification of the corresponding analytical apparatus. This tractable and digestible approach allows for increase of accuracy, sensitivity, responsiveness, and functional ranges in the synthesized precision elastic systems.