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- W2026168047 abstract "A Spherical kinematic differential geometry can be analyzed by use of Darboux frame three times. Firstly, the spherical movement of a rigid body is analytically expressed as the differential moving of Darboux frame of a given spherical curve, and the instant velocity center can be located by letting the velocity be zero, which leads to form both the moving centrode and the fixed centrode. Secondly, the trajectories, traced by points of the moving body, are examined and expressed in the Darboux frame of the centrodes, which establish the connections among the spherical movement of the rigid body, the point-trajectory and the position of the point in the moving body. Thirdly, the invariants of point-trajectories, like the curvatures and its derivatives in second and third orders, are derived by the differential formulas of the Darboux frame of the point-trajectory, but their local properties are also discussed in the Darboux frame of the centrodes, such as the geodesic Euler-Savary equation of a trajectory and the special points of the moving body, the cusp point, the geodesic inflection point, the geodesic curvature stationary curve, geodesic Ball point, and spherical Burmester points and so on. And then, the global properties of coupler curves are discussed for spherical four-bar linkages, such as, the double point, oval curve, symmetrical curve, etc and the distribution of coupler curves are revealed in the numeral examples." @default.
- W2026168047 created "2016-06-24" @default.
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- W2026168047 date "2015-05-15" @default.
- W2026168047 modified "2023-09-27" @default.
- W2026168047 title "Spherical Kinematic Differential Geometry" @default.
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- W2026168047 doi "https://doi.org/10.1002/9781118255056.ch4" @default.
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