AI 中文总结
本文结合代数与几何方法的优势，基于共形几何代数逆运动学模型分析通用3R机器人，提出研究其四个逆运动学解条件的框架，给出一类正交机器人的充要条件。
AI 中文摘要
过去已有多种方法对通用3R机器人的运动学分析展开研究。代数方法已取得具体成果，但遗憾的是仅局限于特殊类别或结构简化情况；而几何方法则将分析扩展至通用机器人，同时能直观理解其运动学特性。我们结合两种方法的优势，利用基于共形几何代数方法得到的逆运动学模型，开展通用3R机器人的运动学分析。本文提出一种通用框架，用于研究3R机器人具有四个逆运动学解（IKS）的条件，还可分析工作空间中IKS的分布情况；并利用所提方法给出一类正交机器人的充要条件。
英文摘要
The kinematic analysis of a generic 3R robot has been investigated with multiple approaches in the past. The algebraic approaches have established concrete results but are unfortunately limited to special classes or architectural simplifications. Geometric approaches on the other hand have extended the analysis to generic robots while also providing an intuitive understanding of their kinematic properties. We use the best of both approaches to present the kinematic analysis of a generic 3R robot, using the inverse kinematic model inherited from a method based on conformal geometric algebra. The paper discusses a generic framework to study the conditions for a 3R robot to have four inverse kinematic solutions (IKS) and allows to study the distribution of IKS as seen in workspace. The necessary and sufficient conditions for a class of orthogonal robots are presented using the proposed approach.
Journal refIn: Holderbaum, W., Selig, J.M. (eds) Advances in the Mathematics of Robotics. IMA 2025. Springer Proceedings in Advanced Robotics, vol 39. Springer, Cham
DOI：10.1007/978-3-032-10510-3_9
