Our paper arose from the desire to physically build a single track vehicle that would solve drawbacks of classic designs, while keeping all their advantages. Bringing such large task to success requires a strategy and, most of all, a method. The paper is mostly about the strategy of separation of concerns. We separate the theory, the design aspects and the construction. Our method is in being explicit about decisions that we make, and recording every step of our calculations. This first paper, of three, examines all that can be known about the motion of a single wheel, in a hope that its properties would carry over to vehicles with two or more wheels in line. The paper also lays down the notations and concepts of the theory as they are used in all three papers. The next paper deals with design of vehicles with multiple wheels in line. The final one deals with issues of construction.
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