arXiv:2610.17272v1 Announce Type: new Abstract: This paper addresses trajectory tracking for a class of nonlinear mechanical systems with input delay. The delayed actuator channel is represented as an equivalent transport partial differential equation, thereby transforming the original delayed system into a coupled plant-channel representation. A finite-dimensional approximation of the delay channel is then constructed through Galerkin projection, resulting in an explicit ODE model of the delayed actuator dynamics. Using this reduced-order plant-channel model, a backstepping controller is developed, and Lyapunov analysis establishes uniform exponential stability of the nominal tracking error dynamics for the reduced-order Galerkin model. To enhance practical implementation, a command-filtered version is also introduced to avoid direct differentiation of virtual controls, for which a corresponding uniform ultimate boundedness result is obtained. Simulation studies are provided to validate the proposed design and illustrate the effectiveness of the method.