Falls among middle-aged and elderly individuals are a significant public health issue. Understanding the mechanisms behind human balance is crucial for effectively addressing these problems. This paper proposes a coupled model that integrates the ankle, knee, and hip joints with a balance board. Bifurcation analysis of the model was performed using DDE-Biftool software, yielding local stability results in a parameter space. Nonlinear numerical analysis was conducted on parameter points within domains of different stability characteristics. The results provided insights into the motion behaviors and patterns of the model under various conditions of balance board stiffness and proprioceptive feedback, such as stability properties, oscillation amplitude, oscillation frequency, and convergence speed.