EE 521 Kinematics and Dynamics of Machines

This course is designed to equip students with fundamental theories and computational methodologies that are used in (computer aided) analysis of multibody systems. Students will learn how to analytically formulate dynamics equations for multibody systems as well as how to utilize numerical algorithms to simulate such systems. Computational mechanics is of high value for the purposes of performance evaluation, sensitivity studies, control system design, model based monitoring and so on.

Students will be introduced to generalized coordinates and speeds, analytical and computational determination of inertia properties, generalized forces, Kane’s method, Lagrange’s equations, holonomic and nonholonomic constraints. Computerized symbolic manipulation and time integration methods for dynamic analysis will be exercised.

Of the available techniques for formulating equations of motion for multibody systems, symbolic formulation and Kanes method will be emphasized. Being a vector based approach and making optimal use of generalized coordinates and speeds, Kane’s method is preferred for its relative ease of computerization and its computational efficiency. Efficiency may be interpreted here both as producing equations efficiently (with the fewest symbolic operations) and producing efficient equations (which require the fewest numerical operations for their solution). Also, Kanes method produces equations in ordinary differential form (ODEs) even for non-holonomically constrained systems, which can be accommodated using (stabilized) standard solvers. The emphasis in this course is not on the excessive mathematical abstraction but rather on an integrated understanding of modeling, equation derivation and numerical solution. A solid understanding of the principles of dynamics in the context of modern analytical and computational methods is aimed.

This course is designed to equip students with fundamental theories and computational methodologies thatare used in (computer aided) analysis of multibody systems. Students will learn how to analytically formulatedynamics equations for multibody systems as well as how to utilize numerical algorithms to simulate suchsystems. Computational mechanics is of high value for the purposes of performance evaluation, sensitivitystudies, control system design, model based monitoring and so on.Students will be introduced to generalized coordinates and speeds, analytical and computational determina-tion of inertia properties, generalized forces, Kane’s method, Lagrange’s equations, holonomic and nonholo-nomic constraints. Computerized symbolic manipulation and time integration methods for dynamic analysiswill be exercised.

Of the available techniques for formulating equations of motion for multibody systems, symbolic formulationand Kanes method will be emphasized. Being a vector based approach and making optimal use of gener-alized coordinates and speeds, Kane’s method is preferred for its relative ease of computerization and itscomputational efficiency. Efficiency may be interpreted here both as producing equations efficiently (with thefewest symbolic operations) and producing efficient equations (which require the fewest numerical operationsfor their solution). Also, Kanes method produces equations in ordinary differential form (ODEs) even fornonholonomically constrained systems, which can be accommodated using (stabilized) standard solvers.

The emphasis in this course is not on the excessive mathematical abstraction but rather on an integrated un-derstanding of modeling, equation derivation and numerical solution. A solid understanding of the principlesof dynamics in the context of modern analytical and computational methods is aimed.