Infinitesimal bendings of a toroidal surface of revolution

1968 ◽  
Vol 9 (3) ◽  
pp. 370-373 ◽  
Author(s):  
K. M. Belov
Keyword(s):  
Surface Of Revolution ◽  
Toroidal Surface

Real-time CAD-level surface of revolution reconstruction on visual slam

2020 ◽  
Author(s):  
Feng Li ◽  
Bin He ◽  
Gang Li ◽  
Ming Ma ◽  
Jian Li ◽  
...  
Keyword(s):  
Real Time ◽  
Level Surface ◽  
Visual Slam ◽  
Surface Of Revolution

scholarly journals Darboux Transforms of a Harmonic Inverse Mean Curvature Surface

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Katsuhiro Moriya
Keyword(s):  
Mean Curvature ◽  
Curvature Surface ◽  
Surface Of Revolution ◽  
Darboux Transforms

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäcklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution.

Workspace Cusp Locations, and Simplified Workspace Boundary Equations for General RRR Regional Structures of Manipulators

1996 ◽  
Author(s):  
Peregrine E. J. Riley ◽  
Louis E. Torfason
Keyword(s):  
Complex Geometry ◽  
Spatial Location ◽  
Polynomial Equation ◽  
Toroidal Surface ◽  
General Complex ◽  
Cusp Points ◽  
Joint Variable ◽  
Boundary Equations ◽  
Workspace Boundary

Abstract General, complex geometry forms of RRR regional structures are often avoided due to the presence of inner boundaries within the workspace which tend to complicate robot guidance. Despite the added complexity, certain RRR geometries may have useful applications as they contain large workspace regions where four alternate configurations may be used to reach a given spatial location. Cusp points often appear on the workspace boundaries of general RRR regional structures, and determining their precise location may be useful for both design and guidance purposes. A twelfth degree polynomial equation in the outer joint variable is derived which defines the location of non-trivial cusps in the workspace. A new closed form workspace boundary equation is derived in the outer joint variable and x coordinate of the toroidal surface generated by rotation of the two outer revolutes. If the outer joint variable is incremented, a quadratic in x is formed at each step which enables a very efficient determination of the workspace boundaries while also providing the coordinates of the boundary on the toroidal surface.

Null testing toroidal surface and biconic surface with cylinder compensator

2013 ◽  
Vol 11 (s2) ◽  
pp. S22202-322206
Author(s):  
Zhuang Liu Zhuang Liu ◽  
Yan Gong Yan Gong
Keyword(s):  
Toroidal Surface
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