Group theoretic approach to large-deformation property of three-dimensional bar-hinge mechanism

Abstract

A group-theoretic approach is presented for investigation of large-deformation property of bar-hinge mechanisms with dihedral symmetry in three-dimensional space. The number of the compatibility conditions at bar-ends is reduced by formulating them with respect to the null space of the linear compatibility matrix. It is shown that the system of reduced compatibility equations inherits the group equivariance from the original compatibility equations. This inheritance is used to develop a method to judge whether the frame has a finite mechanism mode. Sufficient conditions for large deformation mechanisms are derived based on the symmetry properties of infinitesimal mechanism modes and generalized self-equilibrium force modes. The detailed procedure of the method is shown through the numerical examples.