6. Unified Rigid Sub-chain Detection for Planar Kinematic Chains

The detection of rigid sub-chains is crucial in the synthesis of kinematic chains to avoid wasted effort. This chapter introduces the loop superposition method, a unified approach to detect rigid sub-chains in both simple and multiple joint kinematic chains, as well as planetary gear trains. The method leverages Euler's Theorem to reduce the number of sub-chains considered, making the process more efficient. The chapter provides a step-by-step guide to implementing this method, highlighting its advantages over existing techniques and its potential to improve the design of mechanisms.