Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2020 / Cilt: 16 - Sayı: 2

The Forward Kinematics of Rolling Contact of Timelike Curves Lying on Timelike Surfaces

Pages
215–224
Publication Date
2020-06-24
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This study does not take sliding motion into consideration but applies a new Darboux frame method to establish the kinematics of spin-rolling motion.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of the present study is to investigate the forward kinematics of spin-rolling contact motion of one timelike surface on another timelike surface along their timelike trajectory curves in Lorentzian 3-space.
📊
Key Findings & Data:The aim of the present study is to investigate the forward kinematics of spin-rolling contact motion of one timelike surface on another timelike surface along their timelike trajectory curves in Lorentzian 3-space.
💡
Conclusion & Impact:This study does not take sliding motion into consideration but applies a new Darboux frame method to establish the kinematics of spin-rolling motion.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Darboux frame · forward kinematics · Lorentzian 3-space

Abstract

The aim of the present study is to investigate the forward kinematics of spin-rolling contact motion of one timelike surface on another timelike surface along their timelike trajectory curves in Lorentzian 3-space. This study does not take sliding motion into consideration but applies a new Darboux frame method to establish the kinematics of spin-rolling motion.

🔖

Cite This Article

AYDINALP, M., KAZAZ, M., UĞURLU, H. H. (2020). The Forward Kinematics of Rolling Contact of Timelike Curves Lying on Timelike Surfaces. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 16 - Sayı: 2, 215–224. https://ajindex.com/articles/34986

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (2)

  1. . Agrachev, AA, Sachkov, YL. An intrinsic approach to the control of rolling bodies, in Proc. 38th IEEE Conf. Decis. Control, Phoenix, AZ, USA; 1999, pp 431–435. [2]. Birman, GS, Nomizu, K. 1984.
  2. Trigonometry in Lorentzian Geometry, Ann. Math. Month., 91(9): 543-549. [3]. Bottema, O, Roth, B. Theoretical Kinematics; North-Holland Publ. Co.: Amsterdam, 1979; pp 556. [4]. Cai, C, Roth, B. On the spatial motion of rigid bodies with point contact, in Proc. IEEE Conf. Robot. Autom.; 1987, pp 686–695. [5]. Cai, C, Roth, B. 1986. On the planar motion of rigid bodies with point contact, Mech. Mach. Theory, 21: 453–466. [6]. Chelouah, A, Chitour, Y. 2003. On the motion planning of rolling surfaces, Forum Math., 15(5): 727–758. [7]. Chitour, Y, Marigo, A, Piccoli, B. 2005. Quantization of the rolling-body problem with applications to motion planning, Syst. Control Lett., 54(10): 999–1013. [8]. Cui, L, Dai, JS. 2010. A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects With Point Contact, IEEE Trans. Rob., 26(2): 383–388. [9]. Cui, L. Differential Geometry Based Kinematics of Sliding-Rolling Contact and Its Use for Multifingered Hands, Ph.D. thesis, King’s College London, University of London, London, UK, 2010. [10]. Cui, L, Dai, JS. 2015. A Polynomial Formulation of Inverse Kinematics of Rolling Contact, ASME J. Mech. Rob., 7(4): 041003_041001-041009. [11]. Do Carmo, MP. Differential Geometry of Curves and Surfaces; Prentice-Hall: Englewood Cliffs, New Jersey, 1976. [12]. Karger, A, Novak, J. Space Kinematics and Lie Groups; STNL Publishers of Technical Lit.: Prague, Czechoslovakia, 1978. [13]. Li, ZX, Canny, J. 1990. Motion of two rigid bodies with rolling constraint, IEEE Trans. Robot. Autom., 6(1): 62–72. [14]. Marigo, A, Bicchi, A. 2000. Rolling bodies with regular surface: Controllability theory and application, IEEE Trans. Autom. Control, 45(9): 1586–1599. [15]. Montana, DJ. 1995. The kinematics of multi-fingered manipulation, IEEE Trans. Robot. Autom., 11(4): 491–503. [16]. Müller, HR. Kinematik Dersleri; Ankara Üniversitesi Fen Fakültesi Yayınları, 1963. [17]. Neimark, JI, Fufaev, NA. Dynamics of Nonholonomic Systems; Providence, RI: Amer. Math. Soc., 1972. [18]. Nelson, EW, Best CL, McLean, WG. Schaum’s Outline of Theory and Problems of Engineering Mechanics, Statics and Dynamics (5th Ed.); McGraw-Hill: New York, 1997. [19]. O’Neill, B. Semi-Riemannian Geometry with Applications to Relativity; Academic Press: London, 1983. [20]. Ratcli