Graph theory based efficiency method and self-locking analysis of epicyclic gear trains

Abstract

Epicyclic gear trains are widely employed in medical devices and robotic joints, where stringent safety requirements must be ensured. Consequently, investigating the self-locking characteristics of such systems holds significant importance. This study proposes a graph-theoretic approach for efficiency analysis by constructing fundamental loops. First, a hierarchical graph-theoretic model is derived from the schematic representation of the gear system, and a loop matrix is established based on the fundamental loops within the model. Subsequently, kinematic and static analyses are performed to obtain angular velocity and torque vector matrices. By modifying the values of input and output components within these vectors, both forward and reverse angular velocities and torques are determined, enabling the formulation of efficiency expressions under different power flow conditions. Further investigation of the self-locking interval reveals that the forward efficiency reaches its maximum only when i₀ = 1.0411, and that reducing the value of i₁ enhances forward efficiency. This provides an analytical approach for improving forward efficiency while ensuring that the output of the gear train remains resistant to reverse motion induced by external reaction forces.