Point-hyperplane frameworks, slider joints, and rigidity preserving transformations

Eftekhari, Yaser; Jackson, Bill; Nixon, Anthony; Schulze, Bernd; Tanigawa, Shin‐ichi; Whiteley, Walter

doi:10.48550/arxiv.1703.06844

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2018

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“…Motivated by numerous potential applications, notably in mechanical engineering, rigidity has also been considered for frameworks with various kinds of pinning constraints [4,8,13,14,16]. Most relevant to this paper is the work of Streinu and Theran [14] on slider-pinning, which we describe below.…”

Section: Introductionmentioning

confidence: 99%

Rigidity of Linearly Constrained Frameworks

Cruickshank

Guler

Jackson

et al. 2018

International Mathematics Research Notices

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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.

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