Advanced design strategies and applications for enhanced higher-order multisegment denatured Pascal curve gears

The existing Pascal curve gears are limited by inflexible pitch curves and constrained transmission ratio changes, which hinders the application in a range of mechanical systems that require more adaptable gear solutions. To address this, a design procedure for higher-order multisegment denatured Pascal curve gear is proposed. A unified mathematical expression for the Pascal curve gear family is derived, enabling the construction of non-circular gears with free-form pitch curves by adjusting key parameters and offering more flexible pitch curve and a wider range of transmission ratios. Compared with elliptical gears and eccentric circular gears, its transmission ratio range can be expanded by up to 35%. Then the transmission characteristics of these gears are analyzed in detail. To validate the design, the visual analysis and design software of the gear is compiled based on Visual Basic, and is verified with the example. The novelty Pascal curve gears is applied to drive the differential velocity vane pump. The displacement, instantaneous flow rate, and pulsation rate of the differential velocity vane pump are calculated. The comparison with the differential pumps driven by eccentric non-circular gears and Fourier non-circular gears shows that when the pitch curves are not concave, the displacement driven by Pascal curve circular gears is the highest (compared to differential pumps driven by eccentric non-circular gears, and Fourier non-circular gears, their flow rates increased by 50.6%, and 175.7%, respectively), and the instantaneous flow pulsation rate of single pump is the smallest.This study shows that the higher-order multisegment denatured Pascal curve gear provides a viable solution for systems requiring flexible transmission mechanisms and improved operational performance.