A Multibody System Approach for the Systematic Development of a Closed-Chain Kinematic Model for Two-Wheeled Vehicles

Abstract

In this investigation, a closed-chain kinematic model for two-wheeled vehicles is devised. The kinematic model developed in this work is general and, therefore, it is suitable for describing the complex geometry of the motion of both bicycles and motorcycles. Since the proposed kinematic model is systematically developed in the paper by employing a sound multibody system approach, which is grounded on the use of a straightforward closed-chain kinematic description, it allows for readily evaluating the effectiveness of two alternative methods to formulate the wheel-road contact constraints. The methods employed for this purpose are a technique based on the geometry of the vector cross-product and a strategy based on a simple surface parameterization of the front wheel. To this end, considering a kinematically driven vehicle system, a comparative analysis is performed to analyze the geometry of the contact between the front wheel of the vehicle and the ground, which represents a fundamental problem in the study of the motion of two-wheeled vehicles in general. Subsequently, an exhaustive and extensive numerical analysis, based on the systematic multibody approach mentioned before, is carried out in this work to study the system kinematics in detail. Furthermore, the orientation of the front assembly, which includes the frontal fork, the handlebars, and the front wheel in a seamless subsystem, is implicitly formulated through the definition of three successive rotations, and this approach is used to propose an explicit formulation of its inherent set of Euler angles. In general, the numerical results developed in the present work compare favorably with those found in the literature about vehicle kinematics and contact geometry.

A Tube Model Predictive Control Method for Autonomous Lateral Vehicle Control Based on Sliding Mode Control

“…In Figure 1, (x, y) is the coordinate of the rear axle axis B, (x f , y f ) is the coordinate of the front axle axis A, l is the axle length between the front and rear wheels, P is the instantaneous rotation center, and R is the rotation radius. The kinematic system of the vehicle can be constructed as follows [32]:…”

Vertical Balance of an Autonomous Two-Wheeled Single-Track Electric Vehicle

“…However, the use of simplified models allows authors to use ad hoc methods, i.e., obtaining a particular solution of a more complex problem. An example of this is the study of the vehicle stability through its handlebar rotation [23].…”

The Differential Transform Method as an Effective Tool to Solve Implicit Hessenberg Index-3 Differential-Algebraic Equations

“…Di erential-algebraic equations (DAEs) are systems formed by di erential and algebraic equations. Simulations of models from various elds such as mechanical systems [1][2][3], vehicle industry [4,5], bio-mechanics [6], machinery [7], aircraft landing gears [8], towed rockets [9], and unmanned aerial vehicles (UAVs) [10,11] often lead to DAEs. DAEs are classi ed by a natural number called the index which has several de nitions.…”

“…e organisation of this manuscript is as follows: in Section 2, we review the Adomian polynomials and the DTM to solve ordinary differential equations. Next, in Section 3, we present the new proposed algorithms to solve the implicit Hessenberg index-3 DAE initial-value problem (1) and (2).…”