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

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Listed:
  • Cumali Ekici
  • Yasin Ünlütürk
  • Mustafa Dede
  • B. S. Ryuh

Abstract

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.

Suggested Citation

  • Cumali Ekici & Yasin Ünlütürk & Mustafa Dede & B. S. Ryuh, 2008. "On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-19, March.
    • Handle: RePEc:hin:jnlmpe:362783
    DOI: 10.1155/2008/362783
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