Penalty Formulations for the Dynamic Analysis of Elastic Mechanisms

A series of penalty methods are presented for the dynamic analysis of flexible mechanisms. The proposed methods formulate the equations of motion with respect to a floating frame that follows the rigid body motion of the links. The constraint conditions are not appended to the Lagrange’s equations in the form of algebraic or differential constraints, but inserted in them by means of a penalty formulation, and therefore the number of equations of the system does not increase. Furthermore, the discretization of the equations using the finite element method leads to a system of ordinary differential equations that can be solved using standard numerical algorithms. The proposed methods are valid for three dimensional analysis and can be very easily implemented in existing codes. Furthermore, they can be used to model any type of constraint conditions, either holonomic or nonholonomic, and with any degree of redundancy. A series of mechanisms composed of elastic members are analyzed. The results demonstrate the capabilities of the proposed methods for simulation analysis.