Week 3 – Vector Algebra and Vector Polygons

This week’s episode builds on the foundational concepts introduced in Week 2 to focus on the practical analysis of planar mechanisms. While Week 2 covered the core definitions of position, posture, and displacement, here we apply those tools to actual mechanical systems. The episode explores how to describe the path, or locus, of a moving point and determine its position using vector notation, considering absolute and apparent positions from different reference frames. It also demonstrates the posture of a rigid body—its combined position and orientation—using analytical and graphical techniques such as loop-closure equations and complex algebra. Practical applications, including slider-crank mechanisms, internal combustion engines, and train driving wheels, illustrate the importance of understanding these kinematic principles in real-world mechanisms.

The content was created using an AI notebook, with material adapted from textbook excerpts, lecture slides, and worked examples to form a clear and structured learning resource.