On the exact equation of inextensional, kinematically indeterminate assemblies

An exact equation describing the finite displacements of assemblies consisting of rigid bars and pin joints is presented. A numerical procedure is proposed for carrying out the calculations, and some examples are shown in order to illustrate the procedure. To depict the finite change of state, a system of non-linear algebraic equations must be solved. With linear approximation, finite node coordinate increments can be used. This is one of the advantages of the proposed procedure in contrast with the compatibility differential equation description, where only infinitesimal increments can be used. The procedure can be applied even for the analysis of pin-jointed space frames in the post-critical regime, also in the calculation of certain mechanisms of mechanical engineering.