A Reduced and Linearized High Fidelity Waveboard Multibody Model for Stability Analysis

Abstract

In this paper, the robustness of a recently validated linearization approach is demonstrated with the linear stability analysis of a waveboard, a human-propelled two-wheeled vehicle consisting in two rotatable platforms, joined by a torsion bar and supported on two caster wheels. A multibody model with holonomic and nonholonomic constraints is used to describe the system. The nonlinear equations of motion, which constitute a differential-algebraic system of equations (DAE system), are linearized along the steady forward motion. With this approach, the minimal set of linearized equations of motion of the waveboard multibody model with toroidal wheels is derived. The procedure enables the generation of the Jacobian matrix in terms of the geometric and dynamic parameters of the multibody system, and the eigenvalues of the system are parameterized in terms of the design parameters. The resulting minimum set of linear equations leads to the elimination of null eigenvalues, while retaining all the stability information in spite of the reduction of the Jacobian matrix. The linear stability results of the waveboard obtained in previous work are validated with this approach. The procedure shows an excellent computational efficiency with the waveboard, its utilization being highly advisable to linearize the equations of motion of complex constrained multibody systems.