Multiport representation of inertia properties of kinematic mechanisms

Abstract The practical simplicity of obtaining equations of motion using the methods of Lagrange and Hamilton is lost in the algebra of the Euler-Lagrange equation when many nonlinear constraints exist among the physical coordinates in the energy state functions. Such is the case for mechanical systems containing kinematic mechanisms. This paper presents a technique which produces explicit Lagrange or Hamilton equations for mechanism dynamics suitable for computer solution. A general matrix description of mechanism kinematics and inertial properties permits the algebra of the reduction from physical to generalized coordinates to be performed symbolically or numerically by a digital computer. The physical inertia transformed into properties associated with the generalized coordinates of the mechanism displays both physical and artificial behavior to account for conservation of momentum, kinetic co-energy and energy. The method produces equations efficient for numerical calculation and provides insight into the complex inertial dynamics of mechanisms. Vector bond graphs provide a conceptual basis for the technique and describe the energetic structure of the equations. A numerical example illustrates the procedure and results.