Manufacturing of Gear Rims with Application of Flexagons

Abstract

Flexagons are figures folded from flat strips such as paper. Till present, such figures were used only as toys. We propose to apply flexagons in manufacture of gear rims. First, you need to make a flexagon from a flat strip in the form of a toothed band. The resulting flexagon is fit into the appropriate mold by a spiral or closed rings and it is subjected to axial compression. There are a lot of options for folding the strip into the desired gear band. Qualitatively and quantitatively, the appropriate flexagon is described by our proposed generalized formula: where is the angle of the axis of the fold line; is the angle of rotation of the band at bending; is the bend radius at the inner surface; is another extension of the blank strip along its edge. The advantages of the proposed design and methods for manufacture of gear rims are the pollution-free production, possibility to produce only to teeth of the necessary materials - i.e. saving the quality material; the possibility of making those gear rims, which are difficult to machine by conventional methods: internal teeth, teeth having a non-standard profile, non-circular gearwheels.