For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
Figure 1: Visualizing the matrix transformation process. Deep Dive into the Algorithm In the previous post (Part 1) , we introduced the basic concept and Excel VBA code for the Gauss Elimination Method . In this post, we will look under the hood at the mathematical derivation that makes this algorithm work. Understanding these steps is critical for engineers who want to write their own solvers or understand why simulation software sometimes fails (e.g., division by zero errors). Search for Numerical Methods with MATLAB Advertisement Phase 1: Forward Elimination Why do we call it "Elimination"? Because our goal is to systematically remove variables from equations until we are left with a solvable state. Let's consider the general form of a system of linear equations: Step 1: Normalization The algorithm starts by normalizing the first equation. We divide the entire Equation (1) by...