FEM-Based Generation of Stiffness Maps

In robotics, static stiffness maps are used as tools for the performance analysis of robots employed in production tasks, such as pick-and-place or manufacturing. This paper evaluates the relevance of a numerical tool built from a commercial finite element package to generate stiffness maps for any type of robot (serial, parallel, hybrid or compliant). The key points are the spatial resolution, the precision, and the calculation time of a stiffness map. The method for obtaining the 36 static stiffness maps of a 3-D robotic structure in its operational space is presented. The mechanical model is based on a finite element calculation using beam elements for the links and spring elements for the joints. The approach is first applied to a rigid-body mechanism. Numerical results show that a good compromise can be obtained between spatial resolution, precision, and calculation time. Then, the method is applied to a compliant structure requiring processing in a large displacement framework for the relevant estimation of a stiffness map. The numerical tool opens new prospects for the design of robotic structures, in terms of both optimization and use of various material behaviors.