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A novel gear mechanism named high-order multi-segment deformed eccentric non-circular gear was proposed for achieving the unification of non-circular gears with typical-form pitch curve and non-circular gears with free-form pitch curve. The transmission mechanism of the high-order multi-segment deformed eccentric non-circular gear was analyzed, and the unified mathematical expression of eccentric gears was established. The non-circular gears with free-form pitch curve could be constructed based on the proposed high-order multi-segment deformed eccentric non-circular gear by changing the parameters. Moreover, the transmission characteristics were discussed, such as the transmission ratio relationship, convexity distinguished conditions, curvature radius of pitch curve. The visual design and simulation software and generation software of tooth profile for non-circular gears are compiled based on MATLAB, and was verified with the example. This novelty gear was applied to the drive mechanism of the metering pump. The mathematical model of non-circular gear-crank slider mechanism is established and the 3D model and virtual prototype experiment of the mechanism are accomplished. The application showed that the high-order multi-segment deformed eccentric non-circular gears were feasible in practice. [ABSTRACT FROM AUTHOR]