Stiffness Matrix Synthesis Algorithms for Pre-loaded Planar Structures

Abstract — The force regulation and inevitable positional inaccuracy of traditional control system can be compensated by the compliance/stiffness mechanism. 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 manipulate the stiffness matrix into a particularly simple form using matrix algebra. Based on the canonical form of the stiffness matrix, the authors present two novel synthesis procedures for the desired non-symmetric stiffness matrix of planar structures when the structure is not in equilibrium.