Polynomial Systems Arising in Paradoxical $6R$ Linkages

Appears in collection : 2023 - T3 - WS2 - Geometry of polynomial system solving, optimization and topology

In this talk, we first provide a comprehensive definition of closed n-linkages and explain their mobility, typically denoted as $n-6$. We then focus on the intriguing subset of closed n-linkages with mobility higher than $n-6$, known as paradoxical linkages. Based on the powerful tools of Bond Theory and the freezing technique, we present a thorough classification of n-linkages with mobility of $n-4$ or higher, incorporating revolute, prismatic, or helical joints. Additionally, we explicitly derive strong necessary conditions for $nR$-linkages with mobility of $n-5$. Utilizing these necessary conditions, we explore and discuss possible polynomial systems that arise in paradoxical $6R$ linkages.

Information about the video

Date of recording 17/10/2023
Date of publication 17/10/2023
Institution IHP
Language English
Audience Researchers
Director(s) Alexandre Duplessis
Format MP4
Venue Amphitheater Hermite, IHP

Citation data

DOI 10.57987/IHP.2023.T3.WS2.004
Cite this video Li, Zijia (17/10/2023). Polynomial Systems Arising in Paradoxical $6R$ Linkages. IHP. Audiovisual resource. DOI: 10.57987/IHP.2023.T3.WS2.004
URL https://dx.doi.org/10.57987/IHP.2023.T3.WS2.004

Domain(s)

Robotics

Bibliography

Duarte Guerreiro, T., Li, Z. & Schicho, J. Classification of higher mobility closed-loop linkages. Annali di Matematica 202, 737–762 (2023). https://doi.org/10.1007/s10231-022-01258-y