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This book covers the fundamental aspects of kinematic analysis and synthesis of linkage, and provides a theoretical foundation for engineers and researchers in mechanisms design. The methodology and procedure presented is systematic and comprehensive. It presents for the first time a complete curvature theory from planar motion to spatial motion based on centrodes/axodes using the differential geometry language, and the adaptive approach for kinematic synthesis of planar and spatial linkages based on the curvature theory and curve/surface fitting. This opens up a new approach to kinematic analysis and synthesis of linkages. The authors guide the reader through a logical sequence from simpler to more complex cases, dealing with planar, spherical and spatial motion. The theory and tools required for analysis are first presented and then applied to case studies, enabling the reader to follow the process through three topics - adaptive curve fitting, generalized curvature and the adjoint approach.