KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2022 / Cilt: 15 - Sayı: 1

On the Configurations of Closed Kinematic Chains in Three-dimensional Space

Gerhard ZANGERL
Alexander STEİNİCKE
Sayfa
96–115
Yayın Tarihi
2022-04-30
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

To demonstrate the practical feasibility of the new method, we present numerical examples.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints.
📊
Temel Bulgular & Veri:In special cases, we can find a new set of parameters that describe the diagonal lengths (the distance of the joints from the origin) of the configuration space by a simple domain, namely a cube of dimension $n-3$.
💡
Sonuç & Katkı:To demonstrate the practical feasibility of the new method, we present numerical examples.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Configuration space · closed kinematic chain · closed continues random walk

Abstract

A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three dimensions. We investigate the space of configurations, described in terms of joint angles of its spherical joints, that satisfy the the loop closure constraint, meaning that the kinematic chain is closed. In special cases, we can find a new set of parameters that describe the diagonal lengths (the distance of the joints from the origin) of the configuration space by a simple domain, namely a cube of dimension $n-3$. We expect that the new findings can be applied to various problems such as motion planning for closed kinematic chains or singularity analysis of their configuration spaces. To demonstrate the practical feasibility of the new method, we present numerical examples.

🔖

Bu Makaleye Atıf Yap

ZANGERL, G., STEİNİCKE, A. (2022). On the Configurations of Closed Kinematic Chains in Three-dimensional Space. International Electronic Journal of Geometry, Cilt: 15 - Sayı: 1, 96–115. https://ajindex.com/articles/672055

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (13)

  1. Baker, M.: Matt Baker’s Math Blog. https://mattbaker.blog/2018/06/25/the-balanced-centrifuge-problem/. Accessed: 2021-07-15
  2. Brunnthaler, K., Schröcker, H., Husty, M.: A new method for the synthesis of bennett mechanisms. Proceedings of CK2005, Cassino, (2005)
  3. Chansu, S., Taewoong, T., Beobkyoon, K., Hakjong, N., Munsang K., Park, F.: Tangent space rrt: A randomized planning algorithm on constraint manifolds. In Robotics and Automation (ICRA), 2011 IEEE International Conference on, pages 4968–4973,(2011)
  4. Chirikjian, G.: A new inverse kinematics algorithm for binary manipulators with many actuators. Advanced Robotics, 15:20, (2000).
  5. Cortes, J., Simeon, T.: Sampling-based motion planning under kinematic loop closure constraints. In Proc. of Workshop on Algorithmic Foundations of Robotics, (2004)
  6. Creemers, T., Celaya, E., Ros, L.: Exact interval propagation for the efficient solution of planar linkages. In Proc. of the 12th World Conference in Mechanism and Machine Science, (2007)
  7. David, B., Nir, S.: Generic singular configurations of linkages. Topol. Appl. 159(3),877–890 (2012).
  8. Hausmann, C., Knutson, A.: The cohomology ring of polygon spaces. Ann. Inst: Fourier (Grenoble), 48,281–321 (1998)
  9. Hegedüs, G., Schicho, J., Schröcker, H.: Four-pose synthesis of angle-symmetric 6r linkages. J. Mech. Robot. 7(4), (2015). https://doi.org/DOI: 10.1115/1.4029186 [10] Hinokuma, T., Shiga, H.: Topology of the configuration Space of polygons as a codimension one submanifold of a torus. Publ. RIMS, Kyoto Univ. 34, 313–324 (1998).
  10. Husty, M., Pfurner, M., Schröcker, H.: A new and efficient algorithm for the inverse kinematics of a general serial 6r manipulator. Mech. Mach Theory. 42(1),66–81 (2007).
  11. Husty, M., Pfurner, M., Schröcker, H., Brunnthaler, K.: Algebraic methods in mechanism analysis and synthesis. Robotica. 25(6),661–675 (2007)
  12. Iosif, B., Husty, M., Calin, V., Bogdan, G., Tucan, P., Doina, P.: Joint-space characterization of a medical parallel robot based on a dual quaternion representation of SE(3). Mathematics, 8(7), 1086 (2020).
  13. Jaillet, L., Porta, J.: Path planning under kinematic constraints by rapidly exploring manifolds. IEEE Trans. Robot. 29(1),105–117 (2013). https://doi.org/10.110