Validation of a Dynamic Simulation of a Five Degree of Freedom Point Contact Joint
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A new special case computer simulation to model the non-linear, three dimensional dynamic equations of motion of a five degree of freedom point contact joint has been developed and the functionality has been validated with data collected from a physical model. A system physically realistic to model was designed with sphere in sphere contact. A small outboard body articulates within a larger inboard spherical cut out body and springs help provide stability to the system by attaching the outboard body to the ground. The outboard body can move relative to the inboard body in both a rolling and sliding manner. The dynamic equations of motion were determined using Kane’s formulation and a numerical solution was attained through the implementation of a fourth-fifth order, variable time step, Runge-Kutta integrator. The positions of four markers, located on the outboard body of the system, were predicted in ground fixed coordinates by the solution routine. A physical model of the system was constructed and position locations of four markers located on the outboard body were captured by an Optotrak 3020 motion tracking system. Both static and dynamic experimental trials were performed and compared to the simulation. For one test case, the experimental data frequency of oscillation was found to be ωe = 2.33 Hz and the simulation frequency was found to be ωs = 2.37 Hz. Several sources for the discrepancies include viscous damping, a possible additional forcing function caused by lead wire sway, and neglecting the mass of the system’s springs. Coulomb damping was included in the simulation.