Stiffness Matrix Analysis and Synthesis for Pre-Loaded Planar Structures

The compliance/stiffness of a robotic mechanism is usually modeled by a 6 by 6 symmetric positive definite matrix at an equilibrium point using screw theory. When an external wrench is exerted on the mechanism and the mechanism moves away from its equilibrium, the modeled compliance/stiffness matrix becomes non-symmetric. In this article, the authors derive a non-symmetric stiffness matrix for a robotic mechanism and present a novel synthesis procedure for the desired non-symmetric stiffness matrix of a planar structure when the structure is not in equilibrium