AN IMPROVED BOUND FOR THE RIGIDITY OF LINEARLY CONSTRAINED FRAMEWORKS

摘要

We consider the problem of characterizing the generic rigidity of bar-joint frameworks in Rd in which each vertex is constrained to lie in a given affine subspace. The special case when d = 2 was previously solved by Streinu and Theran [Discrete Comput. Geom., 44 (2020), pp. 812{837] and the case when each vertex is constrained to lie in an affine subspace of dimension t, and d = t(t was solved by Cruickshank et al. [Int. Math. Res. Not. IMRN, 12 (2020), pp. 3824{3840]. We extend the latter result by showing that the given characterization holds whenever d = 2t.