SPATIAL DYNAMICS OF MULTIBODY TRACKED VEHICLES - PART I - SPATIAL EQUATIONS OF MOTION

In this paper, the nonlinear dynamic equations of motion of the three dimensional multibody tracked vehicle systems are developed, taking in to consideration the degrees of freedom of the track chains. To avoid the solution of a system of differential and algebraic equations, the recursive kinematic equations of the vehicle are expressed in terms of the independent joint coordinates. In order to take advantage of spar se matrix algorithms, the independent differential equations of the th ree dimensional tracked vehicles are obtained using the velocity trans formation method. The Newton-Euler equations of the vehicle components are defined and used to obtain a sparse matrix structure for the syst em dynamic equations which are represented in terms of a set of redund ant coordinates and the joint forces. The acceleration solution obtain ed by solving this system of equations is used to define the independe nt joint accelerations. The use of the recursive equations eliminates the need of using the iterative Newton-Raphson algorithm currently use d in the augmented multibody formulations. The numerical difficulties that result from the use of such augmented formulations in the dynamic simulations of complex tracked vehicles are demonstrated. In this inv estigation, the tracked vehicle system is assumed to consist of three kinematically decoupled subsystems. The first subsystem consists of th e chassis, the rollers, the sprockets, and the idlers, while the secon d and third subsystems consist of the tracks which are modeled as clos ed kinematic chains that consist of rigid links connected by revolute joints. The singular configurations of the closed kinematic chains of the tracks are also avoided by using a penalty function approach that defines the constraint forces at selected secondary joints of the trac ks. The kinematic relationships of the rollers, idlers, and sprockets are expressed in terms of the coordinates of the chassis and the indep endent joint degrees of freedom, while the kinematic equations of the track links of a track chain are expressed in terms of the coordinates of a selected base link on the chain as well as the independent joint degrees of freedom. Singularities of the transformations of the base bodies are avoided by using Euler parameters. The nonlinear three dime nsional contact forces that describe the interaction between the vehic le components as well as the results of the numerical simulations are presented in the second part of this paper.