1. Introduction

The chapter delves into the critical issue of synthesizing planar kinematic chains for mechanism-based products, highlighting the limitations of current methods that rely heavily on researchers' experience and intuition. It introduces a unified method to automatically generate and classify valid topological structures of kinematic chains, ensuring completeness, effectiveness, and designer-friendliness. The method is designed to handle various types of kinematic chains, including simple joint kinematic chains, multiple joint kinematic chains, and planetary gear trains. The chapter also addresses open problems in structural synthesis, such as the need for a complete atlas database, consistent synthesis results, full automation, and a unified synthesis method. The proposed approach aims to resolve these issues and provide a robust foundation for the creative design of mechanisms in different fields, as demonstrated through various case studies.