Simulation of multibody systems is an increasingly-used computer aided engineering tool and has become more accessible through increased use of assembly-based solid modelling software. This module covers the theoretical basis of multibody dynamics, including constraint equations, dynamics formulations and numerical solution methods, and its application to a range of engineering problems using industry standard packages. The theory is presented and applied using simple examples, while more complex systems are implemented using industry-standard simulation environments. Issues such as model complexity, and non-ideal behaviour such as friction, contact and flexibility are considered, as well as the modelling of associated systems such as actuators and controllers. The interaction of mutibody simulation packages with other computer aided engineering tools such as CAD and with other modelling methods such as the finite element method is also considered. Examples are sourced from a range of application areas across mechanical engineering.
Kinematics of multibody systems; Review of kinematics of particles and rigid bodies. Coordinate frames and transformations in 2D and 3D. Degrees of freedom, joints and constraints in multibody systems. Kinematic constraint equations – assembly and solution of kinematic models. Redundancy and degeneracy.
Dynamics of Multibody Systems: Review of dynamics of particles and rigid bodies. The Newton-Euler equations applied to multibody systems. Generalised coordinates and the principle of virtual work. Formulations including Lagrange’s equations and Kane’s equations applied to simple multibody systems. Assembly of dynamics equations for multibody systems.
Numerical Methods: Taylor’s series and the solution of systems of ODEs. The Euler, Runge Kutta and other methods. Variable timestep methods. Stiffness and stability. Implicit and explicit methods commonly used.
System Modelling: Idealisation and modelling of real world systems. Complexity, accuracy and computational effort. Validation. Modelling behaviours such as friction, flexibility, contact. Modelling of control, actuation and other elements. Model creation/import and interaction with other Computer Aided Engineering tools. Alternative model representations.
