Introduction to Multi-body Dynamics

Transcription

1 division Graduate Course ME 244) Tentative Draft Syllabus 1. Basic concepts in 3-D rigid-body mechanics 1. Rigid body vs flexible body 2. Spatial kinematics (3-D rotation transformations) and Euler theorem 3. Newton-Euler equations of motion 4. Moments and products of inertia 2. Inter-connected rigid bodies 1. Kinematic pairs (joints) with classification of constraints 2. Springs, dampers, actuators and controllers with brief introduction of controls theory 3. Formulation of equations of motion for inter-connected bodies 1. Relative coordinates, generalized coordinates, Cartesian co-ordinates 2. Lagrange s equations 3. Differential equations (ODE) 4. Co-ordinate partitioning 5. Types of analyses (kinematic, static, quasi-static, dynamic and linear dynamic) 4. (Optional Extension) Application of numerical methods 1. NR method, Jacobian, ODE integrators (Euler methods and Implicit methods) Besides the above syllabus, lectures will cover extra material pertaining to ME 244 that ME 144 students and strongly recommended to audit, but will not be evaluated for through assignments and quizzes.

2 division Graduate Course) Expected Learning Outcomes This course will bring together students interested in the applied field of computational dynamics. They will extend their understanding of basic particle dynamics and 2-dimensional rigid body mechanics to 3- dimensional rigid bodies and how to analyze interconnected bodies in a multi-body system. After completion of this course, the students will be able to: 1. Derive equations of motion for a rigid body in 3-dimensions. 2. Implement methods of formulating equations of motion for interconnected bodies. 3. Apply their mathematical background in differential equations, vector calculus, linear algebra and numerical methods to analyze multi-body systems. 4. Analyze the static and dynamic behaviors of the multi-body systems. 5. Extend their learning to application areas such as robotics and biomechanics.

3 University of California Merced Graduate Course Request Form Group Submitting Request Mechanical Engineering and Applied Mathematics 1. Course Number Full Course Title: ME 244 Introduction to Multi-body Dynamics Abbeviated Course Title: Intro to Multi-body Dynamics Effective Date Fall 2013 Discontinue Date Number of Units: 4 (Each unit should correspond to an average of 3 hours of student effort per week. For courses with nonstandard formats, justification for the number of units should be provided.) 2. Pre-requisites: 3. Are there co-requisites for the course? No Is this course to be taken concurrently with another course? 4. No 5. Is this course restricted to certain graduate groups? No 6. Course Description Limited to 50 words Rigid body mechanics (Rotation parameterization, Newton-Euler equations, inertia tensor), Interconnected bodies (joints, actuators, controllers), Equations of motion (Lagrange's equations, Lagrange multipliers, body jack, DAEs) and Analyses (kinematic, static, quasi-static, dynamic, kinetostatic, linear-dynamic). Background in vector mechanics, differential equations, numerical methods, linear algebra, MATLAB-Simulink, and Vibrations is necessary.

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5 division Graduate Course ME 244) Tentative Draft Syllabus Everything in the syllabus below will be shared between ME 144 and ME 244 except the parts highlighted in red font. The parts highlighted in the red font are for audit in ME 144 (the undergraduate students will not be evaluated for their performance on them towards their final grade via assignments and quizzes). However, they belong to the performance evaluation criteria of the graduate students towards their final grade. 1. Basic concepts in 3-D rigid-body mechanics 1. Rigid body vs flexible body 2. Spatial kinematics (3-D rotation transformations) 3. Euler theorem, rotation parameterization, Rodriguez formula 4. Newton-Euler equations of motion 5. Moments and products of inertia 2. Inter-connected rigid bodies 1. Kinematic pairs (joints) with classification of constraints 2. Springs, dampers, actuators and controllers with brief introduction of controls theory 3. Formulation of equations of motion for inter-connected bodies 1. Relative coordinates, generalized coordinates, Cartesian co-ordinates 2. Lagrange s equations and other approaches such as body-jack method 3. Differential equations (ODE) and differential algebraic equations (DAE) 4. Co-ordinate partitioning and Lagrange multipliers 5. Types of analyses (kinematic, static, quasi-static, kineto-static, dynamic and linear dynamic) 4. (Optional Extension) Application of numerical methods 1. NR method, Jacobian, ODE integrators (Euler methods and Implicit methods) 2. Stability, accuracy and Dahlquist s tradeoff criteria 3. DAE integrators such as half-explicit methods 4. Stiffness and damping - physical vs numerical 5. Lock-up, bifurcation and singularities