[Submitted on 31 Aug 2026]
Title:Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra
View a PDF of the paper titled Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra, by Abhilash Nayak and 1 other authors
View PDF HTML (experimental)
Abstract:The inverse kinematics of generic 3R robots has been investigated through multiple approaches, mainly algebraic methods involving the solution of certain equation sets. Previous geometric interpretations of the solution, characterized as the intersection of a pair of conics have been confined to the joint-space domain. In this article, we study the Inverse Kinematic Model (IKM) of 3R robots, using the advantages of Conformal Geometric Algebra (CGA) to provide further insights on its kinematic properties. Our approach directly yields a univariate polynomial in terms of theta_2 without the need to eliminate theta_1 and theta_3 by reframing the problem as the intersection of two circles, which are fundamental elements within this algebraic framework.
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2609.00311 [cs.RO]
(or arXiv:2609.00311v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2609.00311
arXiv-issued DOI via DataCite (pending registration)
Journal reference: In: Holderbaum, W., Selig, J.M. (eds) Advances in the Mathematics of Robotics. IMA 2025. Springer Proceedings in Advanced Robotics, vol 39. Springer, Cham
Related DOI:
https://doi.org/10.1007/978-3-032-10510-3_8
DOI(s) linking to related resources
Submission history
From: Durgesh Haribhau Salunkhe [view email] [v1] Mon, 31 Aug 2026 20:01:15 UTC (10,934 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra, by Abhilash Nayak and 1 other authors
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.RO
new | recent | 2026-09
Change to browse by:
cs
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)