Developed Motion of Robot End-Effector of Timelike Ruled Surfaces With Spacelike Rulings (The First Case)

Year 2020, Volume: 2 Issue: 1, 9 - 21, 04.03.2020

Gülnur Şaffak Atalay , Emin Kasap

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
paper, we analyzed the problem of describing trajectory of a robot end-effector
by a timelike ruled surface with spacelike ruling. We obtained the developed frame
 by rotating the
generator frame  at an Darboux
angle  in the plane , which is on the striction curve  of the timelike
ruled surface . Afterword, natural frame, tool frame and surface
frame which is necessary for the movements of robot are defined derivative
formulas of the frames are founded by calculating the Darboux vectors. Tool frame
 are constituted
by means of this developed frame. Thus, robot end effector motion is defined
for the timelike ruled surface  generated by
the orientation vector . Also, by using Lancret curvature of the surface and
rotation angle (Darboux angle) in the developed frame the robot end-effector
motion is developed. Therefore, differential properties and movements an
different surfaces in Minkowski space is analyzed by getting the relations for
curvature functions which are characterized a timelike ruled surface with spacelike
directix. Finally, to be able to get a member of trajectory surface family
which has the same trajectory curve is shown with the examples in every
different choice of the Darboux angle which is used to described the developed
frame. 

     

Keywords

Robot end-effector, Timelike ruled surface

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