Rigid body and coordinate systems, position and orientation, rotation matrices and their properties, Euler angles, quaternions, homogeneous transformation matrices and their properties, examples
Linear and angular velocity of a rigid body, skew symmetric angular velocity matrix, space fixed and body fixed angular velocity, linear and angular acceleration, Coriolis/centripetal acceleration, velocities and accelerations in terms of Euler angles/quaternions, examples
Joints in multi-body systems, joint variables, Degree-of-freedom and constraints due to a joint and in multi-body systems, holonomic and non-holonomic constraints, velocity and acceleration of rigid bodies in a multi-body system, alternate system of coordinates and resulting constraints, examples
Mass and inertia of a rigid body, Properties of inertia matrix, external forces and moments acting on a rigid body -- gravity, friction, actuator torque/forces, angular momentum – example of spinning top and gyroscope.
Free-body diagram, Newton-Euler formulation and equations of motion, Introduction to recursive formulations, examples.
Equations of motion using Lagrangian formulation – rolling of a thin disk in 3D, two link robot and 4-bar mechanism, solution of equations of motion in Matlab, comparison between Newton-Euler and Lagrangian formulation.
Modeling and simulation of multi-body systems using computer tools, examples using Simscape.
Linearization of equations of motion, state space formulation, state variables, solution of state equations
Stability, controllability and observability in SISO systems, examples
Root locus and Bode plots, relationships between classical and state space approaches
Design of controllers using state space and root locus.
Case studies in modeling and control – planar robot, pendulum on a cart, stabilization using gyroscope etc.