Synthesis of the Pitch Surfaces of Non-Circular Skew-Gears

The subject of this paper is the synthesis of the pitch surfaces of non-circular skew gears, intended to generate any motion program with a periodically varying transmission ratio. This is done by extending an existing algorithm, which was formulated through the application of dual algebra and the Principle of Transference. In particular, the variable transmission ratio of N-lobed elliptical and logarithmical cylindrical gears is expressed and analyzed along with their main characteristics to test the proposed algorithm, which is implemented in Matlab. The code generates the pitch surfaces of N-lobed elliptical and logarithmical skew gears, along with those of indexing skew gears. Finally, significant numerical and graphical results are shown to analyze the geometrical characteristics of the gear engagement. Not unexpectedly, cylindrical and bevel non-circular gears become particular cases thereof.