SUMMARY In many chain drives and tracked vehicle system applications, the shape of a closed chain may not significantly change during the functional operation of the system. This paper presents certain approximation methods which assume that the chain shape does not change. Because of the high frequency contact and impact forces, using approximate numerical schemes based solely on the kinematic descriptions of the closed chain, may lead to erroneous results. Different procedures for the numerical solution of the dynamic equations of motion of the tracked vehicles are presented. The tracked vehicles are modeled as two kinematically decoupled subsystems; the first is the chassis subsystem which consists of the chassis, rollers, idlers, and sprockets, and the second is the track subsystem which consists of the track links, interconnected by revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the equations of the two subsystems are not kinematically coupled. The objective of the procedures developed in this investigation is to examine the feasibility of improving computational efficiency by observing that the shape of a track does not significantly change even though its links undergo significant displacements. In such cases the magnitudes of the nonlinear terms propagate along the diagonals of a velocity influence coefficient matrix which is the only source of nonlinearity in the generalized inertia matrix of the track subsystem. Optimized numerical methods, based on coordinate permutations and reduction of the degrees of freedom of the track chain, are introduced and their effectiveness in the dynamic modeling of tracked vehicles is examined. Numerical results obtained using the two methods of coordinate prediction and coordinate reduction are presented and compared to the results obtained using the recursive kinematic equations in which all degrees of freedom of the track chain are considered. The analysis procedure developed in this investigation is applied to only a planar tracked vehicle model.
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