Topological mechanics explores mechanical deformations and elastic vibrations inspired by principles of topology and symmetry. By extending concepts from condensed matter topology, we focus our investigation on fundamental theory and leverage advanced numerical computations to predict and analyze mechanical behaviors. Our work includes 3D printing and experimental verification, ensuring that theoretical models are matched by practical applications. This interdisciplinary research aims to create materials and structures with unprecedented control over mechanical properties, paving the way for innovative technologies in fields such as metamaterials, materials science, and structural engineering. Through our synergy of theory, computation, and experiments, topological mechanics offers a transformative approach to understanding and manipulating mechanical systems.