Exceptional Stewart--Gough Platforms, Segre Embeddings, and the Special Euclidean Group

DOI10.1137/17M1114284zbMath1455.65076OpenAlexW2793707609MaRDI QIDQ4564018

Charles W. Wampler, Samantha N. Sherman, Jonathan D. Hauenstein

Publication date: 12 June 2018

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1114284

zbMATH Keywords

Segre embeddingnumerical algebraic geometryspecial Euclidean groupStewart-Gough platformarchitecturally singular

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Kinematics of mechanisms and robots (70B15) Computational aspects of higher-dimensional varieties (14Q15) Numerical algebraic geometry (65H14)

Related Items (2)

A numerical toolkit for multiprojective varieties ⋮ Noetherian operators and primary decomposition

Uses Software

• Macaulay2
• Bertini
• StewartGoughGenus7

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Witness sets of projections
• Regenerative cascade homotopies for solving polynomial systems
• Efficient path tracking methods
• Numerical elimination and moduli space of vacua
• Architecturally singular planar parallel manipulators.
• Unification and extension of intersection algorithms in numerical algebraic geometry
• The degree of \(\text{SO}(n,\mathbb{C})\)
• Bond theory for pentapods and hexapods
• Mobile icosapods
• Membership tests for images of algebraic sets by linear projections
• Architecturally singular non-planar parallel manipulators
• Parallel robots.
• A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations
• Minimally rigid periodic graphs
• Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials
• Adaptive Multiprecision Path Tracking
• A family of exceptional Stewart-Gough mechanisms of genus 7
• Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets
• Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
• Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science

This page was built for publication: Exceptional Stewart--Gough Platforms, Segre Embeddings, and the Special Euclidean Group