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In this paper, a twisting-based consensus algorithm is put forward to deal with the event-triggered finite-time consensus for networked Lagrangian systems with directed graphs. First, a fully distributed event-triggered finite-time protocol is considered, for which we can show that each agent can achieve the consensus after a settling time. In order to remove the requirement of continuous monitoring, a pull-based triggering mechanism is employed. Simultaneously, the Zeno-behavior can be excluded under a finite-time dynamic condition. Then, due to the advantages of non-chattering behaviors and finite-time convergence, a twisting-based consensus algorithm based on homogeneous techniques is developed to drive the Euler-Lagrange systems to the consensus value in a settling time. By means of Pólya's theorem and Sum of Squares tools, a polynomial Lyapunov function is constructed to verify our criteria. At last, we give a numerical example for 2-DOF prototype manipulators to verify the validity of the theoretical results.