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

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...

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Bibliographic Details
Published in:Mathematical Problems in Engineering 2008-01, Vol.2008 (2008), p.348-366
Main Authors: Ekici, Cumali, Ünlütürk, Yasin, Dede, Mustafa, Ryuh, B. S.
Format: Article
Language:English
Subjects:
Curvature
Differential geometry
End effectors
Euclidean space
Geometry
Mathematical problems
Methods
Partial differential equations
Robot dynamics
Robots
Studies
Theory
Vectors (mathematics)
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2008/362783