The simulation of elastic mechanisms using kinematic constraints and Lagrange multipliers

Abstract

In the Lagrange multiplier method, the motion of each element is represented in terms of its own rigid-body and flexible body generalized coordinates. The elements are treated as uncoupled from each other except for the application of interaction forces (the Lagrange multipliers) which enforce constraint conditions between the elements. Rather than eliminating the multipliers and obtaining coupled system coordinates, the values of the Lagrange multipliers are solved in time as part of a numerical technique. The multipliers are applied in turn to the individual elements and the simulation proceeds to the next point in time using numerical integration. The method of solution is applied to an illustrative example, a slider-crank mechanism. Modeling considerations and appropriate kinematic constraints are discussed. The author hopes to present numerical results for this example at the conference.