In this article, a state-coupled neural network (SDNN) is proposed to solve the distributed multiple robotic arms (DMRAs) synchronous collaboration problem. The synchronized collaboration of DMRAs is not only in the Cartesian space of the end-effector but also in the corresponding joint velocity space to keep the joint velocity synchronized. First, the constraints for motion generation of leader and follower robots are obtained based on the desired trajectory and communication topology, respectively. Then, the DMRAs collaboration is transformed into quadratic programming based on the minimum velocity norm index. Second, a novel SDNN is designed based on the communication topology of the DMRAs to solve the quadratic programming problem, and the stability of the SDNN is proved by the Lyapunov method. Finally, simulations and experiments demonstrate that SDNN can solve the synchronized collaboration problem of DMRAs with unique advantages.