An approach for designing a developable and minimal ruled surfaces using the curvature theory

Güler, Fatma

doi:10.1142/s0219887821500158

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…Firstly, the authors define a sequence of ruled surfaces associated with the trajectory ruled surface and secondly use dual vector algebra to transform the differential geometry of ruled surfaces into that of spherical curves. There has recently been an ascending interest regarding curvature theory [21][22][23][24]. Since the curvature properties in curvature theory characterize a point trajectory, the curvature theory is quite useful for the path planning of robot trajectory.…”

Section: Introductionmentioning

confidence: 99%

Surface family interpolating a common spherical indicatrix curve

Bayram¹,

Güler²,

KASAP³

2023

Preprint

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The trajectory of a moving particle in space forms a curve. By moving a line along a curve, a surface called ruled surface is obtained. The striction point on a ruled surface is the foot of the common normal between two consecutive generators or ruling. The set of striction points defines the striction curve. In the present paper, we obtain surfaces passing through the spherical indicatrix curves formed on the unit sphere by the end points of the geodesic Frenet frame formed on this curve. We present conditions for these curves to be asymptotic curves or geodesic on the surface. We illustrate the method with several examples.

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Section: Introductionmentioning

confidence: 99%

Surface family interpolating a common spherical indicatrix curve

Bayram¹,

Güler²,

KASAP³

2023

Preprint

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“…Since ruled surfaces have a particularly simple structure, they are important for use in many fields such as architecture, engineering, mechanics, kinematics and CAD computer aided design, etc. as well as differential geometry [1,3,6,7,15].…”

Section: Introductionmentioning

confidence: 99%

“…After this work, it's made many articles by different authors on parallel-like surfaces. In 2010, Saglam and Kalkan have 868 S. YURTTANCIKMAZ searched parallel-like surfaces in E 3 1 Minkowski space [12]. In 2015, Yurttançıkmaz and Tarakcı have established a relationship between focal surfaces and parallel-like surfaces.…”

Section: Introductionmentioning

confidence: 99%

On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$

YURTTANÇIKMAZ

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this paper, it has been researched curves lying on parallel-like surfaces $M^{f}$ of the ruled surface $M$ in $E^{3}$. Using the definition of parallel-like surfaces it has been found parametric expressions of parallel-like surface of the ruled surface and image curve of the directrix curve of the base surface. Moreover, obtaining Darboux frames of curves lying on surfaces $M$ and $M^{f}$, it has been compared the geodesic curvatures, the normal curvatures and the geodesic torsions of these curves.

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Offset Trajectory Planning of Robot End Effector and its Jerk with Curvature Theory

Güler

2021

Int. J. Comput. Methods

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Some situations that change the parameters of the kinematic structure may cause the robot end effector to deviate [Merlet [2005] Parallel Robots, Vol. 128 (Springer Science & Business Media, Germany)] from the desired trajectory. This effect is called the robustness of the robot by Merlet. One of the ways to correct the robustness is by updating the robot trajectory. The jerk vector of the robot end effector is the third-order positional variation of the TCP and defined as thus the time derivative of the acceleration vector. If there is a high curvature on the transition curve trajectory of robot, then there is a tangential jerk along the trajectory. In this study, the geometrically offset trajectory of the robot end effector from the current trajectory was obtained by using the curvature theory. The angular velocity and angular acceleration of the offset trajectory were calculated. An example of the main trajectory of robot end effector and its offset is given. Also, the jerk of the robot end effector of the offset trajectory was calculated according to the curvature of the trajectory surface in case of a jerk problem caused by a high curvature in the transition curve along the offset trajectory curve.

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An approach for designing a developable and minimal ruled surfaces using the curvature theory

Cited by 3 publications

References 6 publications

Surface family interpolating a common spherical indicatrix curve

Surface family interpolating a common spherical indicatrix curve

On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$

Offset Trajectory Planning of Robot End Effector and its Jerk with Curvature Theory

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