通用3R位置机器人的逆运动学求解：共形几何代数方法
Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra
AI总结：
该研究针对通用3R位置机器人的逆运动学问题，采用共形几何代数（CGA）方法，将问题转化为两圆交点求解，直接得到关于θ₂的单变量多项式，无需消去θ₁和θ₃，拓展了逆运动学的几何解释并简化了求解过程。
AI中文摘要：
通用3R机器人的逆运动学已通过多种方法研究，主要是涉及特定方程组求解的代数方法。此前对该解的几何解释被描述为一对圆锥曲线的交点，且仅局限于关节空间域。本文研究3R机器人的逆运动学模型（IKM），利用共形几何代数（CGA）的优势，进一步探究其运动学特性。本文方法直接得到关于θ₂的单变量多项式，无需消去θ₁和θ₃，而是将问题重新构建为两个圆的交点，这是该代数框架中的基本元素。
英文摘要：
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.
