Analyzing the Stability Problem of Chairs from the Perspective of Force Equilibrium

The chair stability model is an important mathematical tool for analyzing the stability of chair placement. Its core lies in accurately judging the risk of chair tipping and quantitatively evaluating the placement stability.This study innovatively constructs a physical-mathematical coupling model based on the theory of rigid body static equilibrium. By defining the height function of chair legs off the ground and the contact force distribution function, and combining with the mathematical zero-point theorem, it is strictly proved that on a ground satisfying continuity conditions, there must exist a specific rotation angle that can achieve simultaneous four-leg grounding.The model deeply analyzes the simplification mechanism of symmetric structures on moment equilibrium equations, and numerical simulations verify the accuracy and reliability of the theoretical derivation. The research results provide important theoretical basis and methodological guidance for fields such as furniture structural optimization design and robot foot configuration improvement.