Rigidity of linearly constrained frameworks

Cruickshank, James and Guler, Hakan and Jackson, Bill and Nixon, Anthony Keith (2020) Rigidity of linearly constrained frameworks. International Mathematics Research Notices, 2020 (12). pp. 3824-3840. ISSN 1073-7928

[thumbnail of LIN_constrained_frameworks_rigid_26_06_18]
PDF (LIN_constrained_frameworks_rigid_26_06_18)
LIN_constrained_frameworks_rigid_26_06_18.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (327kB)


We consider the problem of characterising the generic rigidity of bar-joint frameworks in R d in which each vertex is constrained to lie in a given affine subspace. The special case when d = 2 was previously solved by I. Streinu and L. Theran in 2010. We will extend their characterisation to the case when d ≥ 3 and each vertex is constrained to lie in an affine subspace of dimension t, when t = 1, 2 and also when t ≥ 3 and d ≥ t(t−1). We then point out that results on body-bar frameworks obtained by N. Katoh and S. Tanigawa in 2013 can be used to characterise when a graph has a rigid realisation as a d-dimensional body-bar framework with a given set of linear constraints.

Item Type:
Journal Article
Journal or Publication Title:
International Mathematics Research Notices
Additional Information:
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version James Cruickshank, Hakan Guler, Bill Jackson, Anthony Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices, Volume 2020, Issue 12, June 2020, Pages 3824–3840, https://doi.org/10.1093/imrn/rny170 is available online at: https://academic.oup.com/imrn/article-abstract/2020/12/3824/5067960
Uncontrolled Keywords:
ID Code:
Deposited By:
Deposited On:
12 Jul 2018 13:50
Last Modified:
17 Sep 2023 02:19