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In this paper fundamental analytical results for automobile lateral stability are developed. Specifically, the linear two degree-of-freedom, fixed steering control, front wheel steer and four wheel steer automobiles with a time lagged lateral tire force model is employed in the analysis. The stability conditions are derived using Routh Hurwitz criterion and Lyapunov’s method. The results are mainly algebraic in nature and examples are given demonstrating potential problems of front wheel and four wheel steering vehicles due to the time lag in the tire’s lateral force.

This paper deals with estimating the lateral stability region of a nonlinear 2 DOF vehicle via Lyapunov Second Method and the non-Lyapunov methods of tangency points and trajectory reversal. The nonlinearity of the model is incorporated in an analytical expression for the lateral tire force. It is shown that the derived analytical expressions for equilibrium points defines the outer limits of the stability region.

Several new mathematical models of a rider ATV system are developed. These new models allow the ATV to have either three or four wheels, the rider to be placed at any orientation relative to the vehicle, and the ATVs wheels to rotate. These models are used to investigate the simulated motion of an ATV system over a bump profile. For each model, overturning stability plots are generated as a function of the rider's side lean angle and the vehicle's initial velocity. These results show that the four-wheeled ATV system is more stable than the three-wheeled ATV system over the bump profile. In addition, the inclusion of wheel rotation only slightly improves the overturning stability of the ATV system and this improvement occurs only at high vehicle speeds.

The term “recreational vehicles” refers to many different types of vehicles from motorhomes to trailers to ATVs. The results presented in this paper apply only to on-highway, self-powered vehicles such as motorhomes, pickup/camper trucks, or conversion vans. Because recreational vehicles come in a vide variety of sizes and shapes and because the utility of the vehicle dictates certain design restrictions care must be taken to insure that these vehicles handle as safely as reasonable possible. In addition, the companies who manufacture recreational vehicles are. generally fairly small firms when compared to automotive manufacturers and do not have large research and development departments. Thus, a need exists for simple analytical expressions which the recreational vehicle designer can use to determine the effects that various parameter changes may have on the stability of the vehicle.

The nonlinear dynamical equations governing a thirteen degrees-of-freedom mathematical model of a three-wheeled all-terrain vehicle/rigid-rider system are formulated in this paper. The system is composed of seven rigid bodies. The vehicle has front mechanical suspensions as well as independent rear swing-arm mechanical suspensions. At the time of this writing, no three-wheeled all-terrain vehicle of this configuration is known to exist. Hence, parameter values for this vehicle were obtained through educated engineering estimations based on information available for other three-wheeled vehicles and other engineering data.

This paper is the second in a series on three-wheeled all-terrain vehicle with full suspension. It investigates and compares the roll, pitch and vertical motions of a thirteen degrees-of-freedom mathematical model of a vehicle/rider system with full mechanical suspensions and a six degrees-of-freedom system with no mechanical suspensions. The three different bump profiles - rectangular, parabolic and sinusoidal - employed in the excitation of the system in Ref. (1)* were used for this system. The results show that the current system has substantially reduced roll, pitch and vertical displacements. As a result, it is better in ride and handling as compared to the previously simulated system (1).

Recreational vehicles have been and are being built in many sizes and shapes. The potential for lateral instability exists among these possible configuations. This paper develops a new, analytical, lateral stability result which incorporates the effects that steer angle, tractive force location and front to rear weight distribution have on steady-state turning. This new analytical result can be easily and quickly evaluated saving valuable time and money for the recreational vehicle designer. Several examples are given demonstrating the usefulness of the result.

This paper presents the dynamical equations of motion governing a six degrees-of-freedom mathematical model of a three-wheeled all-terrain vehicle/rigid-rider system. The parameter values associated with two commercially available three-wheeled all-terrain vehicles, a 1980 Honda ATC 110D and a 1980 Kawasaki KLT 200, are presented. In addition, tire properties such as non-rolling vertical stiffness, cornering stiffness and damping ratio for a 22×11-8 Ohtsu tire and a 22×11-8 Goodyear tire are given. These parameter values are used to simulate the motions of the vehicle/ rider system with the results presented in Part II (1)*

This paper is the second in a series on three-wheeled all-terrain vehicles and investigates the handling and ride characteristics of the six degrees-of-freedom mathematical model of a vehicle/rigid-rider system with no suspension. This vehicle/rider system was simulated over three different bump profiles of rectangular, parabolic and sinusoidal shapes. The results show that a light vehicle/rider system equipped with a set of stiff tires has the poorest handling and ride characteristics whereas a heavy vehicle/rider system equipped with a set of soft tires has the best handling and ride characteristics. It was also shown that, for the particular profiles selected, a longer ramp-like bump profile disturbed the vehicle/rider sytems significantly more than a shorter length bump profile.

Pedal powered vehicles have been and are being built in many sizes and shapes. Due to the wide variety of possible configurations, the potential for lateral stability problems exists. This paper develops a basic analytical result for the lateral stability of rider/cycle systems. This result is algebraic in nature and can be evaluated quickly and easily. Several examples are given demonstrating the potential problems associated with changes in the rider/cycle parameters.

Presently, there exist two classical analytical results that provide information regarding the lateral stability of car/trailer systems. These results are the directional stability equation for the automobile and the frequency and damping relationships for yaw oscillations of a trailer towed by a vehicle of infinite mass. Neither of these classical results provides an adequate description of car/trailer dynamic behavior because the associated classical models do not allow for any car/trailer interaction. In this paper, basic analytical results for car/trailer lateral stability are developed. These results are validated by comparing critical speeds predicted by the new analytical solution with those obtained numerically using a standard eigenvalue technique. General observations based upon the analytical results are then presented.

Comparisons are made between a three wheeled vehicle with two wheels on the front axle, a three wheeled vehicle with two wheels on the rear axle, and a standard four wheeled vehicle. Each vehicle’s lateral stability, rollover stability during lateral acceleration, rollover stability while braking in a turn, and rollover stability while accelerating in a turn are determined. It is shown that for lateral stability, the three wheeled vehicle with two wheels on the rear axle is more stable than the four wheeled vehicle, which is in turn more stable than the three wheeled vehicle with two wheels on the front axle. For rollover stability the four wheeled vehicle is always stable as long as the vehicle’s track width is greater than twice its center of mass height. The three wheeled vehicles are less stable than the four wheeled vehicle in terms of rollover stability.

A comprehensive three dimensional model of the human head and neck is formulated. This model predicts the center of mass displacements, velocities, and accelerations of the head and neck resulting from contact and/or inertial impact forces. Key anatomical components are incorporated in this model along with a joint stopping mechanism. Known acceleration profiles are inputed to the torso and/or head force time histories are specified. The equations of motion are then derived using d'Alembert's form of Lagrange's Principle and are numerically integrated using a fourth order Runge-Kutta technique. Validation is accomplished by the comparison of responses from (i) direct frontal and occipital impact experiments on human cadavers, and (ii) sled tests conducted on human volunteers.