On the genus of a hyperplane section of a geometrically ruled surface

1987 ◽  
Vol 147 (1) ◽  
pp. 173-185 ◽  
Author(s):  
Aldo Biancofiore ◽  
Elvira Laura Livorni
Keyword(s):  
Hyperplane Section ◽  
Ruled Surface

scholarly journals A Note on Parametric Surfaces in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

Robot Workspace of a Tool Plane: Part 2—Computer Generation and Selected Design Conditions for Dexterity

1987 ◽  
Vol 109 (1) ◽  
pp. 61-71 ◽  
Author(s):  
J. K. Davidson ◽  
P. Pingali
Keyword(s):  
Ruled Surface ◽  
End Effector ◽  
Plane Part ◽  
Computer Generation ◽  
Robot Workspace

In this paper the algorithm is completed for generation of envelope-surfaces for plane-workspaces of generally proportioned manipulators. Then the ruled surface Ψ is used for adapting the algorithm to 3-R manipulators for which the outermost two axes intersect (a2 = 0). The discriminant D is further developed, and it is used to classify 3-R manipulators, having a2 = 0, into seven Types. Manipulators, which are of Type 7, (i) can provide any orientation to a tool plane σ or (ii), with a fourth appropriately placed R joint and tool plane Σ, can also provide any attitude to the end effector. Design conditions are developed and presented which ensure that a manipulator will possess these properties of dexterity. The conditions are based on coupled motions at all three, or four, axes.

scholarly journals Characteristics of the double-cycled motion-ruled surface of the Schatz linkage based on differential geometry

2014 ◽  
Vol 229 (5) ◽  
pp. 957-964 ◽  
Author(s):  
Lei Cui ◽  
Jian S Dai ◽  
Chung-Ching Lee
Keyword(s):  
Differential Geometry ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Full Rotation ◽  
Kinematic Properties

This paper applies Euclidean invariants from differential geometry to kinematic properties of the ruled surfaces generated by the coupler link and the constraint-screw axes. Starting from investigating the assembly configuration, the work reveals two cycle phases of the coupler link when the input link finishes a full rotation. This leads to analysis of the motion ruled surface generated by the directrix along the coupler link, where Euclidean invariants are obtained and singularities are identified. This work further presents the constraint ruled surface that is generated by the constraint screw axes and unveils its intrinsic characteristics.

Unisecant curves on a general ruled surface

1978 ◽  
Vol 26 (1-2) ◽  
pp. 169-177 ◽  
Author(s):  
Franco Ghione ◽  
Alexandru T. Lascu
Keyword(s):  
Ruled Surface

On the integral invariants of a closed ruled surface

1990 ◽  
Vol 39 (1-2) ◽  
pp. 80-91 ◽  
Author(s):  
Osman G�rsoy
Keyword(s):  
Ruled Surface ◽  
Integral Invariants

scholarly journals On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Cumali Ekici ◽  
Yasin Ünlütürk ◽  
Mustafa Dede ◽  
B. S. Ryuh
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
End Effector ◽  
Timelike Ruled Surface ◽  
Curvature Theory ◽  
Differential Properties

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effector's motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling.

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