Research On The Transmission Theory Of The Paradoxical Gear

In traditional external mesh gears, an idle gear is needed if we want thedriving gear and driven gear rotate at the same direction. The paradoxical gear inthis research is a new form of gear transmission which can co-rotate without anidle gear. It was invented in1988by French engineer Mr.Mercier and applied tothe MERCIER Differential, which have the same function of the "Torsen"Differential, but more simple and effective. Because of its unique transmissioncharacteristics，the application of the paradoxical gear can simplify the structureof the transmission system, meet the request of lightweight and miniaturizationas well as the need for some special transmission forms.The application of the involute profile makes the paradoxical gear have theadvantages of the traditional gear, being separable and the meshing line is astraight line tangent to the base circle. To make the transmission correctly andcontinuously, the paradoxical gear must meet the forward continuoustransmission condition, the reverse continuous meshing condition and the toothnon-interference condition. These are the basic geometry problems of theparadoxical gear transmission.To facilitate engineers design the paradoxical gear, a reasonable geometricdesign system is needed. Based on the study of the transmission characteristicsand realization conditions, we make clear of the sructure of the paradoxical gear.and present the basic paramiters to design a gear, thereby established the geargeometry calculation system. The influence of the angular coefficient on theshape of the tooth profile and the drive performance of the paradoxical gear isdiscussed as well.The gear transmission performances have a major impact on its engineeringapplications. By establishing the mathematical model of the tooth surface, weobtaine the equation of meshing and the equation of contact line. The physicalquantities, the relative speed at the meshing point, normal curvature of the toothsurface, induced normal curvature of the mating surfaces and the relative slidingcoefficient at the contact points, that characterize the gear transmissionperformance are derived.By analysing the force for a pair of paradoxical gears and calculating thelength of the contact line, the formulas for calculating the bending strength oftooth root and contact strength of tooth surface are deduced.