Abstract: A sprocket having a gear tooth valley radius which varies around the sprocket perimeter provides additional gear torque multiplication to a rider, which is especially beneficial when climbing hills. In some embodiments, the sprocket is a bicycle chainring with reduced gear tooth valley radius over at least a portion of the chainring. In other embodiments, the sprocket is a bicycle rear wheel cassette cog with increased gear tooth valley radius over at least a portion of the cassette cog. Regions of both reduced and increased gear tooth valley radius may be present on a given sprocket. The sprocket valley floor surface may be rounded or may include N segments adjoined by N vertices. The segments of the valley floor surface may be curved or straight. The vertices of the valley floor surface may be curved or angled. Embodiments for bicycles and motorcycles are presented.

Abstract: A multi-tiered building structure. The multi-tiered building structure includes a panel member having a pattern of cuts, a pattern of legs, and a pattern of tabs configured to move the panel member between a nonexpanded position, wherein the panel member forms a substantially flat shape, and an expanded position, wherein the panel member forms a substantially stepped shape. The building structure also includes a support structure configured to accept at least one of the pattern of tabs of the panel member and maintain the panel member in the expanded position.

Abstract: A roller chain and sprocket drive with a randomized sprocket which modulates the roller position on the sprocket by varying the radial seating position of the roller while maintaining a constant chordal dimension between seated rollers. The roots between teeth of the sprocket have radii that vary between a nominal radius and a maximum radius and a minimum radius. This variation or randomization is intended to provide a noise modulation effect while avoiding the negative effects of high impact from conventional randomized sprockets.