On the Linear Line Complex and Hyperboloidal Gearing

The concept of a line complex is introduced and then a brief discussion of a linear line complex is given. A linear line complex can be very useful in specifying the spiral angle in hyperboloidal gearing. Ball’s reciprocity condition is used in conjunction with the linear line complex to specify the spiral angle using a system of cylindroidal coordinates. This spiral angle is such that the gear ratio is independent of the pressure angle.