Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields by Azeb Alghanemi, Abeer AlGhawazi

“…The differential geometry of plane curves has many applications in physics especially in mechanics. …”
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Temperature Field Analysis of Grinding Face Gear by Ning Zhao, Jia Zhai, Shaojie Hou, Qian Yang, Tao Yang

“…The principal directions and corresponding curvatures at grinding point on face gear tooth surface are derived according to meshing theory and differential geometry theory. Based on instantaneous elliptic contact theory and grinding heat theory, the theoretical formula of grinding temperature field of face gear is established. …”
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Research of Exoskeleton Trajectory Algorithm based on Homogeneous Differential Equation by Liang Yuhang, Liang Guoxing, Li Zhili, Song Jinpeng, Ren Qichao

“…The kinematical equation of man-machine exoskeletons is established based on differential geometry homogeneous coordinates equation,according to the lower limb motion parameters,the boundary conditions are got,and then the motion trajectory of ankle is drawn by using the Matlab. …”
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Special Kähler geometry and holomorphic Lagrangian fibrations by Li, Yang, Tosatti, Valentino

“…Given a holomorphic Lagrangian fibration of a compact hyperkähler manifold, we use the differential geometry of the special Kähler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent bundle of the base to the total space of a family of minimal rational curves admits a parallel splitting. …”
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MESHING PERFORMANCE ANALYSIS OF TAPERED ROLLER ENVELOPING END FACE MESHING WORM DRIVE (MT) by WEN YuJie, LIAO HongHui, LIU ZaiXin, LI LingYu

“…According to the gear meshing principle and differential geometry principle, the meshing mathematical model of the transmission pair is established, the worm tooth surface equation and meshing function are deduced, and the meshing performance calculation formula is obtained. …”
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Performance Analysis of Gear Honing with Modified TI-Hourglass Worm Honing Wheel by Cai Weili, Zhang Mandong

“…According to the theories of differential geometry and gear meshing,the basic equations for involute helicoids,meshinglines and meshing boundary lines are deduced.Then using MATLAB program,the contact lines and meshing boundary are drawn.The results show that,under the condition of given the parameters of gear workpiece,the distribution of contact lines and meshing boundary lines are influenced by stagger angle and center distance,the actual contact lines are influenced by work half-angle.On the premise of meeting the strength requirements,giving the center distance called modified gear drive and choosing the reasonable stagger angle and half-angle,the honing full gear without axial feed and the well-distributed and uncrossed contact lines can be realized.The problem is solved that in order to realize full gear honing,the axial feed must be adopted with small helical angle and larger center distance must be adopted with large helical angle.…”
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Radar Cross-Section Formulation of a Shell-Shaped Projectile Using Modified PO Analysis by Mohammad Asif Zaman, Md. Abdul Matin

“…The projectile is modeled using differential geometry. The paper presents a detailed analysis procedure for RCS formulation using physical optics (PO) method. …”
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Study on Meshing Characteristic of Face Gear Pair based on Pinion Modified by Continuous Shifting by Zhang Jinzhao, Liu Lei

“…At first,based on the differential geometry theory and the space mesh theory,the tooth surface equations of the modified face gear pair are derived. …”
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Geometric Meshing Simulation Analysis of Zero Spiral Bevel Gear by Zhou Jiaojun

“…Then,the major axis of instantaneous contact ellipse is calculated based on differential geometry. The numerical example results show that,a middle- convex parabolic transmission error with the amplitude under a smaller range is achieved by using the modified roll method. …”
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RESEARCH ON NUMERICAL SIMULATION OF STRESS DISTRIBUTION OF ANTI-TWIST BRAIDED WIRE ROPE by FU Chao, WANG Hui, CUI WeiHua, XU HongQin, ZHAO Xia

“…Applying the differential geometry theory and principle of coordinate transformation,the spatial curve parametric equations were derived. …”
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Study on the High Precision Manufacturing of the Hourglass Worm Drive Pair in the Solar Tracking System by Chen Yan, Gong Yuxia

“…Aiming at the wrong transmission form of the hourglass worm drive in the solar tracking system,based on the differential geometry and the space meshing theory,the accurately mathematical model of involute enveloping hourglass worm is deduced. …”
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The Exact Linearization and LQR Control of Semiactive Connected Hydropneumatic Suspension System by Xuyang Cao, Linlin Cao, Dianlong Wang

“…Based on differential geometry theory, the nonlinear system of connected hydropneumatic suspension was transformed to a linear one. …”
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General Mathematical Model of the Intersecting Cross-axis Gear based on Conjugate Curve by Shuhong Liu, Rulong Tan, Xiaodong Guo

“…In this method， differential geometry and gear kinematics and the conjugate curves meshing theory are applied to deduce the general mathematical model of the conjugate curves intersecting cross-axis gear. …”
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Research of the Tooth Flank Design and Movement Simulation of Spiral Noncircular Bevel Gear by Xu Aifen, Jia Jumin, Chen Yuqing

“…Applied the theory of curve and surface of differential geometry,based on the noncircular bevel gear profile researched and developed successfully by research team. …”
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Pseudoinversion of degenerate metrics by C. Atindogbe, J.-P. Ezin, Joël Tossa

“…A large class of differential operators in differential geometry is intrinsically defined by means of the dual metric g∗ on the dual bundle TM∗ of 1-forms on M. …”
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Research on NC Machining Method of Face Gear in High Speed Milling by Xingzu Ming, Hongyang Wang, Jinwei Shen, Lei Jin, Rui Ming

“…According to the principle of differential geometry and the theory of gear meshing， and with CNC milling machine high speed milling machined face gear as the research object， the mathematical model of straight tooth face gear is established. …”
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Tooth Surface Design and Solid Modeling of Offset Orthogonal Arc Tooth Face Gear by Zhanrong Feng, Lingfeng Gao, Ping Fang, Guangjin Xiong, Chao Luo

“…A certain offset distance is applied to the arc tooth cylindrical gear， which is used as an imaginary tool to envelop the offset orthogonal arc tooth face-gear. Based on the differential geometry calculation and gear meshing principle， the equations of the offset orthogonal arc tooth face-gear surfaces are deduced， and the mathematical models of working tooth surface and transition surface are established in Matlab. …”
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Inverse Fourier Transform in the Gamma Coordinate System by Yuchuan Wei, Hengyong Yu, Ge Wang

“…Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry.…”
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Research on Digital Design and Tooth Shape Optimization of Non-circular Gears Based on Envelope Features by Yongping Liu, Beibei Yun, Yongqiao Wei, Changbin Dong, Zhongtao Ren

“…Based on the principle of gear meshing and differential geometry theory， the motion coordinate conversion relationship between the gear cutter and the non-circular gear tooth blank is obtained， and the machining process of the non-circular gear tooth profile is simulated. …”
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UNDERCUT AND TOOTH PROFILE MODIFICATION OF DOUBLE HELICAL PULLEY by GUO JianHua, LI JianBo, JIANG HongYuan, LI WenHua

“…As for the smooth problems in the conjugate surface arising from hob tooth root and flank arc edge during the processing of new double helical synchronous belt’s pulley,the broken line generation mechanism at the conjugate tooth profile was investigated with spatial differential geometry and meshing theory. Through the undercut boundary curve characteristics analysis of the hob tooth profile surface,the parameter constraint conditions used to eliminate the pulley surface singularity was determined,and the eliminating profile singularity modification method by increasing the transition arc curve slope face on the hob tooth profile was proposed. …”
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