An application of geodesics to the calculation of the rib-thickness of globoidal cam mechanisms

• The geodesics are employed to calculate the rib-thickness of globoidal cams.
• The rib-thickness of globoidal cams is calculated.
• Curves and vectors related to the rib-thickness are derived and simulated.
• We compare the rib-thickness with respect to three motion curves.
• We find that the peak value of velocity has a great effect on rib-thickness.

A systematic approach based on the geodesics in differential geometry for calculating the rib-thickness of the globoidal cam is proposed. In the proposed approach, the analytical description of the rib-thickness is derived and calculated using coordinate transformation, conjugate theory and differential geometry. In addition, the mathematical expressions for the contact curves of the conjugate surfaces, intersection curves of the ribbed surfaces with the torus, and the geodesics of the torus surface are conveniently derived. Then these curves and the ribbed surfaces are all simulated with the help of Creo Software after the calculation results are obtained using VC programming. By comparing the rib-thickness with respect to three motion curves, we find that the peak value of the velocity curve has great effects on the rib-thickness. A globoidal cam used in an automatic tool changer of CNC machines is used as an example to validate the proposed methodology. The results of this research are necessary for both the selection of motion curves, and the investigations of the rigidity and the strength of the globoidal cam mechanisms.