Abstract
Compared with disc-cam mechanisms, cylindrical cam mechanisms have the advantage of shifting the direction of spatial motion transmission. Hence, cylindrical cam mechanisms is quite adequate for realizing the input-output transmission of two non-parallel joint axes. Since the surface of cylindrical cam and that of follower can be regarded as a set of conjugate gear tooth profiles, this research employs the theory of conjugate surface proposed by Litvin for calculating the cylindrical cam profile and apply theory of differential geometry for investigating the characteristics of cam profile. First, this research applies theory of conjugate surface for locating the contact line between the cylindrical cam and the follower at every instant. These contact lines in space form a ruled surface which is the cylindrical cam profile. The research indicates that the pressure angle is larger for the contact points closer to the axis of cam rotation. The force transmission may deteriorate sharply due to larger pressure angles. Therefore, it is recommended to avoid designing the cylindrical cam with smaller inner diameter. In addition, this work addresses two arrangements of the cutting tool for manufacturing cylindrical cams. Both of two arrangements of the cutting tool may result in the deviation of the cam profile at a certain level. Appropriately choosing the way of manufacture may help meet the trade-off between precision and cost. Moreover, the curvature of surface of cylindrical cam profile is analyzed for detecting the undercutting phenomenon. The impacts of design parameters on the undercutting phenomenon are included in this work as well. Finally, we adopt the contact stress theory developed by Hertz for analyzing the maximum contact stress of contact points and calculate the input torque used for driving cylindrical cam mechanisms. In conclusion, the inner diameters of cylindrical cams, subjected to available space, should be designed as larger as possible. Otherwise, a smaller cam size may lead to considerable deviations of cam profile, inefficient force transmission, larger contact stress and undesired undercutting. The present method for designing and analyzing cylindrical cams mechanisms can be comprehensively applicable to other types of spatial cam mechanisms as well.