On the elastostatic analysis of mechanical systems

The subject of this paper is the elastostatic analysis of robot structures. The method of analysis is based on the concept of generalized spring, in which each flexible link is replaced with a six-dimensional generalized spring. The stiffness matrix of this spring, when the link complexity so requires, should be obtained numerically, via finite element analysis (FEA). In this study, a novel formulation for the modeling of all six lower kinematic pairs (LKP), when connecting two flexible links, is introduced. By resorting to this formulation, a compact formula for the stiffness matrix of a parallelogram with flexible linkages, what is called a Π-joint, is obtained. As an illustrative example, the procedure is applied to a Schönflies motion generator that features Π joints. In order to illustrate the online feasibility of the computations involved, the minimum eigenvalues of a dimensionless factor of the stiffness matrix, used as stiffness performance index, are plotted along a standard trajectory adopted by the industry.