Optimization of multibody systems via an energy conserving minimal coordinate formulation

Advances in computer hardware and improved algorithms for multibody dynamics over the past decade have generated widespread interest in realtime simulation of multibody mechanical systems. At the heart of the widely used algorithms for multibody dynamics are a choice of coordinates which define the kinematics of the system, and a choice of time integration algorithms. The current approach uses a non-dissipative implicit Newmark method to integrate the equations of motion denned in terms of the independent joint coordinates of the system. The reduction of the equations of motion to a minimal set of ordinary differential equations is employed to eliminate instabilities associated with the integration of differential-algebraic equations. To extend the unconditional stability of the implicit Newmark method to nonlinear dynamic systems, a discrete energy balance is enforced. This constraint however yields spurious oscillations in the computed accelerations. Therefore, a new acceleration correction is applied to eliminate these instabilities and hence attain unconditional stability. In addition, sensitivity analysis and optimization are applied to create a mechanism design tool. To exemplify the methodology, a wheel loader mechanism is designed to minimize energy consumption subject to trajectory constraints.