SIMPLE COMPATIBILITY EQUATIONS FOR KINEMATIC ANALYSIS OF PIN-JOINTED PLATE MECHANISMS

The erection analysis models of some new spatial structures, such as Pantadome, can be simplified as pin-jointed plate mechanisms. The rigid body displacement of a triangular plate element is characterized by the un-elongation of its three sides due to the shape stability of a triangle. Based on the compatibility equation of a bar element, a simple compatibility equation of a triangular plate element with pin-jointed vertices is established. Its first- and second- order compatibility matrices are presented. By introducing four-vertex coplanar conditions, the compatibility matrices of a quadrangular plate element, which is divided into two triangular plate elements, are further deduced. Theoretically, the compatibility matrix of a planar arbitrarily polygonous plate element can be established by this way. As for the simple compatibility equations, a computational strategy is adopted to track the kinematic path of pin-jointed plate mechanisms. The erection processes of an up-jacked Pandadome and an incrementally-launched gable space frame are numerically simulated. The results indicate that the method presented possesses a high accuracy for solving the kinematic path of pin-jointed plate mechanisms.