Linear Stability Analysis of a Bicycle Multibody Model with Toroidal Wheels

Agúndez, A. G.; García-Vallejo, Daniel; Freire, Emilio

doi:10.1007/978-3-030-81166-2_42

Cited by 3 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case that the matrix 𝑴 ( 𝒙 0 ) is not singular, explicit expressions for the submatrices 𝑱 21 and 𝑱 22 can be found, which are shown in detail in [78]. The size of 𝑱 is 2𝑛 × 2𝑛, leading to 2𝑛 eigenvalues.…”

Section: Symbolic Linearization Of the Index-1 Dae Systemmentioning

confidence: 99%

“…Eccarius et al [69] presented a review of consumer adoption of electric motorcycles, and Manrique et al [70] reviewed the main aspects concerning the kinematics, dynamics and control of two-wheeled vehicles, described within the multibody formulation. Several works in the literature are devoted to the stability of bicycles [14,[71][72][73][74][75][76][77][78], the study of safety and injuries resulting from the use of electric kickscooters [79][80][81][82][83][84][85][86] and the stability of electric kickscooters [87][88][89]. As case studies to illustrate the role of the dependent coordinates in the linearization procedures outlined in this work, the linear stability results of a bicycle and an e-scooter multibody model have been utilized.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Dependent Coordinates in the Linearization of Constrained Multibody Systems: Handling and Elimination

García-Agúndez Blanco,

GARCIA-VALLEJO,

Freire

et al. 2023

Preprint

View full text Add to dashboard Cite

Section: Symbolic Linearization Of the Index-1 Dae Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Dependent Coordinates in the Linearization of Constrained Multibody Systems: Handling and Elimination

García-Agúndez Blanco,

GARCIA-VALLEJO,

Freire

et al. 2023

Preprint

View full text Add to dashboard Cite

An electric kickscooter multibody model: equations of motion and linear stability analysis

Agúndez,

García-Vallejo,

Freire

2024

Multibody Syst Dyn

View full text Add to dashboard Cite

In this work, a detailed multibody model of an electric kickscooter is presented. The model includes toroidal wheels as well as rear and front suspensions. The equations of motion are derived and linearized along the steady forward motion of the vehicle. Using an efficient linearization approach, suitable for complex multibody systems with holonomic and nonholonomic constraints, allows for obtaining the reduced linearized equations of motion as a function of the geometric, dynamic, wheels’, and suspensions’ parameters. The proposed electric kickscooter multibody model is validated with the stability results of a previously presented electric kickscooter benchmark. Since the resulting eigenvalues are parameterized regarding the design parameters, a detailed linear stability analysis of the system is performed. In particular, the influence on the stability of the toroidal geometry of the wheels, the elliptic cross-section of the toroidal wheels, the rider model, the steering axis inclination angle, the inertia tensor of the front frame, and the rear and front suspensions is analyzed. The model presented, together with the linearized equations of motion obtained in this work, enables a systematic analysis of the stability of these vehicles, which helps design new electric kickscooters with improved vehicle safety conditions and oriented to a wider range of potential users.

show abstract

Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints

G. Agúndez,

García-Vallejo,

Freire

2023

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, a detailed and comprehensive linear stability analysis of a rolling toroidal wheel is performed. The wheel is modeled as a rigid toroid-shaped body rolling without slipping on a horizontal surface. The nonlinear equations of motion constitute a Differential-Algebraic Equations system, given by the dynamic equilibrium equations augmented with the nonholonomic constraints, which arise from the no-slip condition. The circular steady motion and the linearized equations of motion along this relative equilibrium are obtained, for both the solid and hollow tori. The expressions of the linearized equations and the corresponding eigenvalues are derived analytically as a function of the torus aspect ratio. The variation of the stability boundary with the torus aspect ratio is shown. A comparison of the results obtained in the solid and hollow scenarios is included, and all the results are validated with the rolling hoop, which corresponds to a degenerate torus with zero aspect ratio. In the particular case of the steady straight-line rolling and spinning about a vertical diameter, which constitute limit motions of the circular steady motion, the critical rotational and angular speeds required for stabilization are obtained.

show abstract

Linear Stability Analysis of a Bicycle Multibody Model with Toroidal Wheels

Cited by 3 publications

References 9 publications

The Dependent Coordinates in the Linearization of Constrained Multibody Systems: Handling and Elimination

The Dependent Coordinates in the Linearization of Constrained Multibody Systems: Handling and Elimination

An electric kickscooter multibody model: equations of motion and linear stability analysis

Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints

Contact Info

Product

Resources

About