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This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics.

Technology: general issues --- History of engineering & technology --- path generation --- dimensional synthesis --- hybrid optimization --- slider-crank mechanism --- hybrid compliant mechanisms --- path analysis --- numerical methods --- elliptic integrals --- kinematics --- Levenberg–Marquardt algorithm --- convergence --- neural networks --- local minima --- optimization --- three-legged parallel mechanism --- compliant mechanism --- flexure-based mechanism --- flexure --- compliant joint --- decoupled motion --- coupled motion --- stiffness --- compliance --- suspension algorithm --- predictive suspension --- land vehicle --- sprung mass --- autoencoder --- aeroengine --- denoising --- GRU --- rotordynamic --- adaptive rejection control --- sinusoidal disturbance --- flexible rotor --- hydrodynamic journal bearing --- six-bar mechanism --- dynamic balancing --- fully Cartesian coordinates --- multiobjective optimization --- differential evolution --- Pareto front --- serial robotic manipulators --- singularity identification --- geometric algebra --- rotor group --- distance to a singularity --- air flow medical sensor --- emergency air flow sensor --- low-cost air flow sensor --- nanostructures --- COVID-19 --- FEM analysis --- biomechanics --- effort mathematical models --- NMR reconstruction --- reverse engineering --- elbow joint --- zipper-coupled tubes --- Miura-ori pattern --- deployable mechanism --- origami inspired design --- smooth sheet attachment --- relative rotation --- jump --- safe basin --- fractal --- heteroclinic bifurcation --- delayed feedback --- helical spring --- vibration --- Frenet trihedral --- dispersion relation --- natural frequency --- approximate entropy --- non-linear systems --- phase space reconstruction --- fault classification --- random forest --- support vector machines --- lateral dynamics --- track parameters --- vehicle mathematical modeling --- safety vehicle index