The FutureForge manipulator and an approximate analytical solution algorithm for its nonlinear dynamics

This paper examines a linearisation algorithm developed for the nonlinear dynamics of the FutureForge manipulator - part of a state-of-the-art forging platform being built in Glasgow, Scotland. Building on previous work, the authors investigate means of obtaining approximate analytical solutions for the highly nonlinear system with a view to developing a practical control system in future work. This is done by a combination of algebraic approximation methods, a practical understanding of the machine’s operating characteristics, as well as the application of a perturbation method. The devised method is verified by comparing the resulting approximate analytical solutions with numerical solutions to the nonlinear problem.