Benchmark Results on the Linearized Equations of Motion of an Uncontrolled Bicycle

In this paper we present the linearized equations of motion for a bicycle as, a benchmark The results obtained by pencil-and-paper and two programs are compaied The bicycle model we consider here consists of four rigid bodies, viz a rear frame, a front frame being the front fork and handlebar assemb...

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Bibliographic Details
Published in:Journal of mechanical science and technology 2005, Vol.19 (1S), p.292-304
Main Authors: SCHWAB, A. L, MEIJAARD, J. P, PAPADOPOULOS, J. M
Format: Article
Language:English
Subjects:
Applied sciences
Benchmarking
Benchmarks
Bicycles
Dynamical systems
Dynamics
Equations of motion
Error correction
Exact sciences and technology
Frames
Fundamental areas of phenomenology (including applications)
Knife-edge
Linearization
Mathematical analysis
Mathematical models
Mechanical engineering. Machine design
Perturbation
Physics
Rigid structures
Roundoff error
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Wheels
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Summary:In this paper we present the linearized equations of motion for a bicycle as, a benchmark The results obtained by pencil-and-paper and two programs are compaied The bicycle model we consider here consists of four rigid bodies, viz a rear frame, a front frame being the front fork and handlebar assembly, a rear wheel and a fiont wheel, which are connected by revolute joints The contact between the knife-edge wheels and the flat level surface is modelled by holonomic constiaints in the normal direction and by non-holonomic constraints in the longitudinal and lateral direction The rider is rigidly attached to the rear frame with hands free from the handlebar This system has three degrees of freedom, the roll, the steer, and the forward speed For the benchmark we consider the linearized equations for small perturbations of the upright steady forward motion The entries of the matrices of these equations form the basis for comparison Three diffrent kinds of methods to obtain the results are compared pencil-and-paper, the numeric multibody dynamics program SPACAR, and the symbolic software system AutoSim Because the results of the three methods are the same within the machine round-off error, we assume that the results are correct and can be used as a bicycle dynamics benchmark
ISSN:1738-494X
1976-3824
DOI:10.1007/BF02916147