Generalized bicycles

Steering in bicycles and motorcycles

Steering a motorcycle or bicycle is counterintuitive; to turn right, you must steer left initially, and vice versa. You can execute this initially counter-directed turn by turning the handlebars explicitly ~called counter-steering! or by throwing your hips to the side. Contrary to common belief, gyroscopic forces play only a limited role in balancing and steering @D. E. H. Jones, Phys. Today 23...

Sampling-based Planning Algorithms Applied to Bicycles

In this paper, I explore the application of various random sampling based algorithms to dynamic models of bicycles. Starting with relatively simple 3-dimensional state space models of bicycle and working up to a more realistic 7dimensional model that incorporates skidding, I examine RRT, RG-RRT, RRT*, and LQR-RRT*.

BMX bicycles: accident comparison with other models.

A comparison has been made between BMX bicycle accidents and those occurring when children ride other types of bicycle. The injuries sustained are compared to see if the clinical impressions that BMX are more dangerous, and produce more facial injuries, are correct. This was found not to be true as half the children involved rode BMX bicycles, and the injuries sustained were similar to those oc...

Benzannulated bicycles by three-component aryne reactions.

Bicycles and left-right tours in locally finite graphs

We extend three results involving bicycles and left-right tours to infinite, locally finite graphs: Read and Rosenstiehl’s tripartition theorem, Shank’s theorem that the residues of left-right tours generate the bicycle space and the planarity criterion of Archdeacon, Bonnington and Little. In order to achieve this it is necessary to allow infinite cycles as defined by Diestel and Kühn.