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

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.

Robotics (cs.RO)

arXiv:2609.00316 [cs.RO]

(or arXiv:2609.00316v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.00316 arXiv-issued DOI via DataCite (pending registration)

In: Holderbaum, W., Selig, J.M. (eds) Advances in the Mathematics of Robotics. IMA 2025. Springer Proceedings in Advanced Robotics, vol 39. Springer, Cham

https://doi.org/10.1007/978-3-032-10510-3_9 DOI(s) linking to related resources