Hypo-paradoxical Linkages: Linkages That Should Move-But Don't

July 27, 2025 Β· Declared Dead Β· πŸ› arXiv.org

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Authors Nir Shvalb, Oded Medina arXiv ID 2507.20371 Category physics.soc-ph Cross-listed cs.RO Citations 0 Venue arXiv.org Last Checked 4 months ago
Abstract
While paradoxical linkages famously violate the Chebyshev-Grubler-Kutzbach criterion by exhibiting unexpected mobility, we identify an opposing phenomenon: a class of linkages that appear mobile according to the same criterion, yet are in fact rigid. We refer to these as hypo-paradoxical linkages, and proceed to analyze and illustrate their behavior. We use the same tools to further explain the unexpected positive mobility of Bennet mechanism.
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