Open AccessOn Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings
Author(s) -
Cumali̇ Eki̇ci̇,
Yasi̇n Ünlütürk,
Mustafa Dede,
Beom-Sahng Ryuh
Publication year - 2008
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2008/362783
Subject(s) - ruled surface , surface (topology) , curvature , robot end effector , motion (physics) , trajectory , generator (circuit theory) , classical mechanics , mathematics , physics , geometry , robot , computer science , artificial intelligence , power (physics) , quantum mechanics , astronomy
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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