Underactuated robots have fewer control inputs than the degrees of freedom of the system. Dynamic model of an underactuated robot considering link flexibility is firstly proposed based on finite element method. Several dynamic coupling indices for underactuated flexible manipulators are analyzed and discussed including acceleration coupling between active and passive joints, dynamic coupling between passive joints and drive torques, and the coupling effect of elastic deformations and joints. The simulation results illustrate that these coupling effects are very important in structure design, configuration design, actuator placement and the control to underactuated robots system, and show that the elastic deformations of links have influence on dynamic coupling indices.

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