Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Toothed gears are the most common mechanical in machine building, which characterized by high reliability and durability, a constant transfer number, can transmit torque. During toothed gear operation, surfaces of teeth slide, gives rise to friction forces wears their working surfaces. To prevent this, need lubrication. This paper considers design tooth engagement, does not have between since they roll over each other without slipping. The profile such is outlined congruent arcs, symmetrical relative line that connects center rotation wheel with top tooth. These curves at intersect predefined angle. In depressions wheel, adjacent also same Such condition be ensured curve all its points crosses radius-vector emanating from coordinate origin, stable angle equal half given one. logarithmic spiral. If number drive driven wheels same, then congruent. Otherwise, profiles would differ but could arcs spiral length taken different areas curve. minimum possible straight. At acute angle, operation impossible. build right tooth, it suffice set wheels. center-to-center distance calculated using derived formula. variable but, an increase teeth, range change decreases. algorithm construction given.