SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2020 / Cilt: 13 - Sayı: 1

On the Configuration Space of Planar Closed Kinematic Chains

Gerhard Zangerl
Pages
74–86
Publication Date
2022-10-18
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)

In order to demonstrate practicality of the new method we present numerical examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A planar kinematic chain consists of $n$ links connected by joints.
📊
Key Findings & Data:In this work we investigate the space of configurations, described in terms of joint angles, that guarantee that the kinematic chain is closed.
💡
Conclusion & Impact:In order to demonstrate practicality of the new method we present numerical examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:configuration space · closed kinematic chain · path planning

Abstract

A planar kinematic chain consists of $n$ links connected by joints. In this work we investigate the space of configurations, described in terms of joint angles, that guarantee that the kinematic chain is closed. We give explicit formulas expressing the joint angles that guarantee closedness by a new set of parameters. Moreover, it turns out that this parameters are contained in a domain that possesses a simple structure. We expect that the new insight can be applied for several issues such as motion planning for closed kinematic chains or singularity analysis of their configuration spaces. In order to demonstrate practicality of the new method we present numerical examples.

🔖

Cite This Article

Zangerl, G. (2022). On the Configuration Space of Planar Closed Kinematic Chains. International Electronic Journal of Geometry, Cilt: 13 - Sayı: 1, 74–86. https://ajindex.com/articles/539601

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Suthakorn, J., Chirikjian, G.: A new inverse kinematics algorithm for binary manipulators with many actuators. Adv. Robotics 15 (2), 225-244 (2000).
  2. Hinokuma, T., Shiga, H.: Topology of the Configuration Space of Polygons as a Codimension One of a Torus. Publ. RIMS, Kyoto Univ. 34 (4), 313-324 (1998).
  3. Hausmann, J. C., Knutson, A.: The cohomology ring of polygon spaces. Ann. Inst. Fourier 48 (1), 281-321 (1998).
  4. Cortes J., Simeon, T.:Sampling-based motion planning under kinematic loop closure constraints. In: Algorithmic Foundations of Robotics VI. Springer (2004).
  5. Celaya E., Creemers, T., Ros, L.: Exact interval propagation for the efficient solution of position analysis problems on planar linkages. Mech. Mach. Theory 54, 116-131 (2012).
  6. La Valle, S. M., Yakey, J. Kavraki, L.: A probabilistic roadmap approach for systems with closed kinemtic chains. In Proc. IEEE Int. Conf. Robot. Autom. (ICRA) 3, 1671-1676 (1999).
  7. La Valle, S. M.:Planing Algorithms. Cambridge University Press (2006)
  8. Han, L., Rudolph, L., Blumenthal, J., Valodzin, I.:Algorithmic Foundation of Robotics VII. Springer, 47, 235-250 (2008)
  9. Han, L., Rudolph, L.: Inverse Kinematics for a Serial Chain with Joints Under Distance Constraints. Robotics: Science and systems, 177-184 (2006)
  10. Han, L., Rudolph, L., Blumenthal, J., Valodzin, I.: Convexly stratified deformation spaces and efficient path planning for planar closed chains with revolute joints. Int. J. R. Res. 27, 1189-1212 (2008).
  11. Milgram, R. J., Trinkle, J. C.: The geometry of configuration spaces for closed chains in two and three dimensions. Homol. Homotopy Appl. 6 (1), 237-267 (2004)
  12. Milgram, R. J., Trinkle, J. C.: Complete path planning for closed kinematic chains with spherical joints. Int. J. R. Res. 21 (9), 773-789 (2002).
  13. Jaillet, L., Porta, J. M.: Path planning under kinematic constraints by rapidly exploring manifolds. IEEE Trans. Robot. 29 (1), 105-117 (2012).
  14. Kapovich, M., Millson, J.: On the moduli spaces of polygons in the euclidean plane. J. Differential Geom. 42 (1), 133-164 (1995)
  15. Liu, G. F., Trink