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Rigidity detection is an important tool for structural synthesis of\udmechanisms, as it helps to unveil possible sources of inconsistency in\udGrübler's count of degrees of freedom (DOFs) and thus to generate\udconsistent kinematical models of complex mechanisms. One case that has\udpuzzled researchers over many decades is the famous "double-banana"\udproblem, which is a representative counter-example of Laman's rigidity\udcondition formula for which existing standard DOF counting formulas fail. The\udreason for this is the body-by-body and joint-by-joint decomposition of the\udinterconnection structure in classical algorithms, which does not unveil\udstructural isotropy groups for example when whole substructures rotate about\udan "implied hinge" according to Streinu. In this paper, a completely new\udapproach for rigidity detection for cases as the "double-banana"\udcounterexample in which bars are connected by spherical joints is presented.\udThe novelty of the approach consists in regarding the structure not as a set\udof joint-connected bodies but as a set of interconnected loops. By tracking\udisolated DOFs such as those arising between pairs of spherical joints,\udrigidity/mobility subspaces can be easily identified and thus the\ud"double-banana" paradox can be resolved. Although the paper focuses on the\udsolution of the double-banana mechanism as a special case of paradox\udbar-and-joint frameworks, the procedure is valid for general body-and-joint\udmechanisms, as is shown by the decomposition of spherical joints into a\udseries of revolute joints and their rigid-link interconnections

Solving the double-banana rigidity problem: a loop-based approach