This paper addresses the dynamic modelling problem for the ECP-750 gyroscope, which is complex nonlinear system with four degrees-of-freedom. It has two actuated and two underactuated joints; the moving of the underactuated joints is the product of the dynamics generated by the actuated joints. The first step to obtain the dynamic model is to development the kinematic model using Denavit-Hartenberg convention, then the dynamic model is obtained by using the analytical mechanics through the motion equations of Euler-Lagrange, we present the main useful properties of the dynamics behavior to design control schemes.
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