Improved design method for line gear pair based on screw theory

The line gear (LG) is a novel gear mechanism based on conjugate space curve meshing theory. It is suitable for micro-mechanical systems due to its small size, light weight, and large transmission ratio. Since its invention, the LG pair has been studied from the perspective of differential geometry. To simplify the design process of the LG pair, we studied the LG pair from the innovative perspective of screw algebra. A unified screw coordinate was created for the LG pair, and velocity screws were established to derive its meshing equations. Moreover, the design equations of the center curves and contact curves were calculated for the driving line teeth and the driven line teeth, respectively. Finally, examples of LG pairs were fabricated for the kinematic performance tests, which indicated that the LG pairs designed according to screw theory were capable of performing a stable transmission.