Hybrid dynamic model for haptic systems with planar mechanisms

The aim of this paper is to present a new partitioning method for solving the equation of motion of a planar mechanism with more than one degree of freedom, using a hybrid dynamic model. The procedure is according to the Newton-Euler formalism with Lagrange equations and can be used in the case that some of the applied forces acting on the elements of the mechanism are unknown, but the time history of generalized coordinate variation (acceleration) of the same elements are imposed. The resulting equations can be used for real time simulations whenever some of the external forces are unknown (but the motion of the same elements are tracked or imposed) and when a high rate of update is expected. For example virtual prototyping with haptic systems needs a very fast haptic rendering loop and forces developed by the user are unknown. Fast simulation makes possible the expansion of the frequency of aliased harmonics of the generated forces in the haptic system, so that it can better mechanically filter them, allowing a wider bandwidth of force. Haptic interaction with an accurate and fast dynamic simulation provides unique insights into the behaviors of the virtual prototype. The proposed partitioning method can be used only in these special circumstances and enforce dynamic consistency over time.