A Fundamental Study on the Involute Spur Gear (Part I)

The purpose of this study is to secure all the reversible gears in ex-or internal gearing. In view of the fact that the theory of this kind hitherto on this question was lacking in examining fully the intervals of parameters used in them, it seems that these gears have not been examined to the minutest details and in the ways of discarding the useless points. Now, to attain this purpose, I will treat of the problem to decide these gears by giving the number of teeth in contact "n", the pressure angle "α", and the gear ratio "ε". Then it follows as a necessary consequence that we will meet the well-known problem on maximum or minimum number of teeth. It is noticeable that we cannot completely solve the problem to decide these gears by giving the number of teeth of both gears z1 and z2, till the above-mentioned problem is solved. In this report I will deal with the case of usual external gearing. And I will state the study for internal gearing in the second report.