Geometric analysis of generic 3R robots, and necessary and sufficient conditions for a class of orthogonal robots to have four IKS

2026-08-31

AI Summary

本文结合代数和几何方法，分析了通用3R机器人的运动学特性，并提出了正交机器人具有四个逆运动学解的充分必要条件。

Abstract

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.

Problem

• 3R robots
• inverse kinematic solutions
• geometric analysis
• orthogonal robots

Innovation

• conformal geometric algebra
• inverse kinematic solutions (IKS)
• geometric and algebraic approaches