A planar mechanical library in the AMESim simulation software. Part I: Formulation of dynamics equations

Abstract

This paper presents the mathematical developments of a planar mechanical library implemented in the AMESim simulation tool. Body and joint components are the basic components of this library. Due to the library philosophy requirements, the mathematical models of the components have required a generic vector calculus based formulation of the constraint equations. This formulation uses a set of dependent generalized coordinates. The dynamics equations are obtained from the application of Jourdain’s principle combined with the Lagrange multiplier method. The body component mathematical models consist of differential equations in terms of the dependent generalized coordinates. The joint component mathematical models are based on the Baumgarte stabilization schemes applied to the geometrical, kinematic and acceleration constraint equations. The Lagrange multipliers are the implicit solution of these Baumgarte stabilization schemes. The first main contribution of this paper is the expression of geometrical constraints in terms of vectors and their exploitation in this form. The second important contribution is the adaptation of existing formulations to the AMESim philosophy.