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On the Configuration Space of Planar Closed Kinematic Chains

Gerhard ZANGERL [1]

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.
configuration space, closed kinematic chain, path planning
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Primary Language en Mathematics Research Article Orcid: 0000-0001-6145-4178Author: Gerhard ZANGERL (Primary Author)Country: Austria Publication Date : January 30, 2020
 Bibtex @research article { iejg611106, journal = {International Electronic Journal of Geometry}, issn = {}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2020}, volume = {13}, pages = {74 - 86}, doi = {10.36890/iejg.611106}, title = {On the Configuration Space of Planar Closed Kinematic Chains}, key = {cite}, author = {ZANGERL, Gerhard} } APA ZANGERL, G . (2020). On the Configuration Space of Planar Closed Kinematic Chains. International Electronic Journal of Geometry , 13 (1) , 74-86 . DOI: 10.36890/iejg.611106 MLA ZANGERL, G . "On the Configuration Space of Planar Closed Kinematic Chains". International Electronic Journal of Geometry 13 (2020 ): 74-86 Chicago ZANGERL, G . "On the Configuration Space of Planar Closed Kinematic Chains". International Electronic Journal of Geometry 13 (2020 ): 74-86 RIS TY - JOUR T1 - On the Configuration Space of Planar Closed Kinematic Chains AU - Gerhard ZANGERL Y1 - 2020 PY - 2020 N1 - doi: 10.36890/iejg.611106 DO - 10.36890/iejg.611106 T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 74 EP - 86 VL - 13 IS - 1 SN - -1307-5624 M3 - doi: 10.36890/iejg.611106 UR - https://doi.org/10.36890/iejg.611106 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Geometry On the Configuration Space of Planar Closed Kinematic Chains %A Gerhard ZANGERL %T On the Configuration Space of Planar Closed Kinematic Chains %D 2020 %J International Electronic Journal of Geometry %P -1307-5624 %V 13 %N 1 %R doi: 10.36890/iejg.611106 %U 10.36890/iejg.611106 ISNAD ZANGERL, Gerhard . "On the Configuration Space of Planar Closed Kinematic Chains". International Electronic Journal of Geometry 13 / 1 (January 2020): 74-86 . https://doi.org/10.36890/iejg.611106 AMA ZANGERL G . On the Configuration Space of Planar Closed Kinematic Chains. Int. Electron. J. Geom.. 2020; 13(1): 74-86. Vancouver ZANGERL G . On the Configuration Space of Planar Closed Kinematic Chains. International Electronic Journal of Geometry. 2020; 13(1): 86-74.

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