A Robust Algorithm for Solving Heterogeneous Systems of Equations Arising in Kinetostatics of Compliant Mechanisms

Abstract

Design and analysis of compliant mechanisms draw constraints from both kinematics and statics, resulting in heterogenous systems of equations. This heterogeneity makes the system numerically ill conditioned and not amenable to the entire solution set (conversely seen for rigid mechanisms), thus burdening Jacobian-based solution procedures and the underlying design or analysis. This article proposes a robust restrained line search for Newton’s method for the numerical solution of such heterogeneous systems. This novel line search (i) prioritizes accuracy of the underlying function approximation over the widely used minimization of the functional residual error and (ii) employs a dual objective function definition with closed-form Hessian formulation to maximize performance. It addresses gaps existing in the classical Newton’s method and makes the method truly localized, even more than the MATLAB’s nonlinear solver “fsolve.” Examples from 2D inverse and 14D coupled kinetostatics of compliant mechanisms are presented to demonstrate the robustness of the proposed algorithm, rendering it into a black-box solver for kinetostatic problems.