The Kinematic Analysis Of Pin-jointed Plate Mechanisms

Under the research background of Pantadome’s construction forming process, the system is abstracted to a pin-jointed plate mechanism consisting of planar plate elements. The analysis method on such mechanism’s rigid motion path and the analytic theory on the kinematic configuration under load are systematically researched in this paper. The main work includes:(1) The basic theory of analysis on mechanisms is systematically introduced. According to the equilibrium matrix rule, it is the condition for the movability of mechanisms that the number of inextensional deformation models is greater than zero. Some methods to track the kinematic path of mechanisms are also briefly described. As for the problem of kinematic bifurcation, the bifurcation point can be predicted by tracing the minimum singular value. Also the second-order compatibility condition is introduced to distinguish the direction of kinematic path. The main research methods for movement forms of load-bearing mechanisms are further listed.(2) The rigid body displacement of triangular plate element is characterized by the un-elongation of its three sides due to the shape stability of triangle. Based on the compatibility equation of bar element, a simple compatibility equation of triangular plate element with pin-jointed vertices is established. By introducing the four-vertex coplanar condition, the compatibility matrices of quadrangular plate element, which is divided into two triangular plate elements, are further deduced. Based on the simple compatibility equations and taking the kinematic analysis method of pin-bar mechanisms for reference, the movability discrimination and kinematic path tracking of pin-jointed plate mechanisms are achieved.(3) The finite element motion equation of triangular pin-jointed plate mechanisms is established. The arc-length method is employed to trace the kinematic path. The stability analysis method which takes the minimum eigenvalue of the tangent stiffness matrix as an index is further expounded. A criterion of whether the singular point is the bifurcation point is put forward, and the accurate positioning method of singular point is proposed. By introducing the interference force vector that depends on the zero space vector of the tangent stiffness matrix, the system makes a movement from the main path to the bifurcation path. Finally the correctness and the effectiveness of the above methods are investigated through an example.