Engagement theory of silent chain mechanism with involute tooth profile

The engagement theory of the gear rack mechanism can be used to study the silent chain mechanism.The modification coefficient of involute sprocket is achieved by the engagement analysis between the silent chain and involute sprocket.The result shows that the variation of the modification coefficient is influenced by the tooth number and the pitch.The variation curve of modification coefficient is given.The undercut of the involute sprocket is investigated to derive the minimum tooth.The research on the minimum and unique modification coefficient proves that the minimum tooth value is 17 as the sproc-ket pitch is equal to 9.525 mm.Based on the envelope principle and the coordinate transformation,the function of the transition curve between the involute tooth profile and root circle is conformed.The approach presented to achieve the modification coefficient and the minimum tooth number is applicable to the silent chain mechanism with all kinds of pitches.