Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra

• URL: http://arxiv.org/abs/2609.00311v1
• Date: Mon, 31 Aug 2026 20:01:15 GMT
• Title: Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra
• Abstract summary: We present the Inverse Kinematic Model (IKM) of 3R robots, using the advantages of Conformal Geometric Algebra (CGA)<n>Our approach directly yields a uni in terms of theta without the need to eliminate theta_3 by reframing the problem as the intersection of two circles.
• Score: 1.654371982203344
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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