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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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Inverse Kinematic Solution for Generic 3R Positional Robots Using Conformal Geometric Algebra

  • 会议论文

  • 发表日期：

    2026年

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  • Abhilash Nayak,
  • Durgesh Haribhau Salunkhe

摘要

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.