Design method of a novel variable speed ratio line gear mechanism

Based on the space curve meshing theory, a novel noncircular line gear mechanism was advanced, namely, this paper presented a design method of the variable speed ratio noncircular line gear with coplanar axes. Firstly, the universal contact curve equations of the constant speed ratio and variable speed ratio line teeth were established. After the constraint equations of the rotating angle of the driving and driven variable speed ratio noncircular line gears were analyzed and established, the relationship between the rotating angle of the driven variable speed ratio noncircular line gear and the parameter t in the VSR area was assumed to be a piecewise fourth-order curve. Then, the contact curve equations of the variable speed ratio noncircular line gears were derived, and the entity models of variable speed ratio noncircular line gears were built. The prototypes of the parallel axis and intersecting axis variable speed ratio noncircular line gears were manufactured by Stereo Lithography Apparatus, and the speed ratios were measured on the kinematic test rig. The kinematic and finite element analysis results demonstrate that the relationship between the rotating angle of the driven variable speed ratio noncircular line gear and the parameter t conforms to the designed function and the noncircular line teeth smoothly achieve the preset VSR transmission. The proposed design method is helpful to design the variable speed ratio noncircular line gears with lower theoretical sliding rate and wider variation range of the speed ratio; consequently, the designed variable speed ratio noncircular line gears have better applicability in specific variable speed ratio applications.