Background: Various relevant papers and patents which have reported non-circular gears are
widely used in many types of mechanical instruments. The Pascal limacon gear is one new type of noncircular
gear. Many researchers have only focused on the design of Pascal limacon gears and their applications.
Little attention has been paid to the machining aspects. Shaping is a better method for fabricating
non-circular gears. The Equal Rotary-Angle of Workpiece Method (ERAWM), the Equal Arc-
Length of Workpiece Method (EALWM), and the Equal Polar-Angle of Workpiece Method (EPAWM)
are the three linkage-methods for shaping Pascal limacon gears. However, which linkage-method
should be chosen in practical has not been studied.
Objective: In order to choose the excellent linkage-methods for shaping Pascal limacon gears, the three
linkage-methods were compared from three aspects: density of shaping cutter trace, uniformity of arc
length of program blocks and control of motion axes of machine tools.
Methods: Firstly, the shaping models of Pascal limacon gears was deduced. Secondly, based on the
mathematical model, shaping linkage-methods of Pascal limacon gears were obtained. Thirdly, under
different shaping linkage-methods, developing regularity of shaping cutter trace, arc length of program
blocks and motion axes of machine tools, were compared.
Results: Finally, the excellent shaping linkage-method EALWM is obtained with the characteristics of
a high density of shaping cutter trace, high uniformity of arc length of program blocks and ease of control.
Conclusion: It has been proven that EALWM is the best linkage-method to shape Pascal limacon gears.