KINEMATICS

ECTS credits: 4

Objectives:

The general objectives of this course are: a) help students visualize and understand actual mechanical configurations with their constraints and practical limitations and, b) provide guidelines to formulate problems and relate theory and practice.

The specific objectives are: a) the ability to analyse the motions in two- and three-dimensions of mechanical systems in realistic conditions and b), apply the theory to classic mechanisms and motion transformers.

Syllabus:

            1 – Theory of Screws (Wrenches) – A simplified approach

• Definitions, sum and moment, shifting equation, scalar invariants, special screws, central axis, Delassus’ theorem.
• Applications to Statics

            2 – Locations of solids – Constraints.

• Definitions: rigid-solids, material and geometrical points, motion, physical frames, and coordinate systems, path of motion, kinematical parameters,
• Location of free solids, Eulerian angles
• Solids submitted to constraints – Classic joints
• Applications to mechanical systems (U-joints, cams, crank-rod, etc.)

            3 – Kinematics of rigid-solids

• Velocity and acceleration of a point
• Velocity field for rigid-solids, kinematical screw, instant angular velocity vector,
• Absolute and relative derivatives of vectors
• Acceleration field for rigid-solids
• Combinations of motions
• Fundamental motions
• Applications to mechanical systems (pumps, systems of bars, U-joints, etc.)

            4 – Contact kinematics

• Point contact kinematics, sliding, rolling, pitching, fundamental properties of rigid-solid kinematics,
• Applications to gear kinematics, planetary gears, differential, rolling element bearings