Novel design method for constrained conjugate contact curves of line gears based on rolling-up of pitch pattern

The line gear is an innovative gear transmission usually manufactured for mini gear boxes in small machines, which is designed according to the meshing theory of three-dimensional conjugate contact curves. In a line gear pair, the rotation of driving and driven contact curves will form a couple of virtual revolving bodies, which are defined as pitch patterns. The shapes of pitch patterns indicate the working space of the line gear pair, and different kinds of driving and driven contact curves will commonly lead to diverse pitch patterns. In this paper, the shapes of the pitch patterns are as given constraints to design the line gears applied in confining space. Several types of two-dimensional curves (straight line, sine curve and logarithmic curve) are rolled up to form varying three-dimensional contact curves, which can occupy the same working space accordingly. To further indicate the features of the obtained contact curves, the pressure angles and the strength of line gears are calculated and compared concurrently with an experiment pertaining to their transmission errors. The test results show that the transmission errors of all the line gear pairs are below 3 %, indicating that the design theory proposed in this paper can efficiently deduce contact curves for the line gear in constrained spaces and consequently extend the application of the line gear in industrial use.