Abstract: The author previously published two papers in the Chinese Journal of Mechanical Engineering, to compare the involute system with the cycloided system, proving that the latter has the following advantages over the former:a) The wear of teeth is uniform in generalb) There are no contact stresses of compression and produced on the teeth;c) The minimum number of the teeth is smallerd) The contact coefficient is larger The present paper also makes a comparison of these two systems and the conclusion is drawn as follows:a) There is almost no difference in contact efficiency of teeth for both systemsb) The amplitude of vibration of the shaft produced by the frictional force between the cycloidal teeth is smaller.