MATLAB for Mechanical Engineers

MATLAB has a series of commands and functions that instruct the program to perform a task. Just like any other programming language, it has a syntax that defines the rules of the symbols and characters used to write a code. It is important for learners to understand the MATLAB syntax, basic commands, and functions to write effective programs.

This week will cover

• MATLAB syntax and commands
• Methods and ways to use commands in different scenarios
• Manipulation of calculations and comparisons
• Use of arrays.
• Functions (plotting, creating animations, creating figures, and more)

Forward kinematics is the process of determining the position of a robot’s end-effector by using kinematic equations with known values of angular velocities and joint parameters. It is important for learners to understand how MATLAB can be used to determine the unknown values in the kinematic equations, as well as simulate the movement of the manipulator.

This week will cover

• Manipulator motion using ImageMagick
• Simulation of a 2R robotic arm manipulator
• Creating a movie clip with the spatial motions of a robotic arm
• ‘For’ loop in programming
• Working of the “hold on” command
• Arrays and linspace commands

The air standard cycle considers air as the working fluid which goes through heat addition and heat rejection. This is a thermodynamic closed loop cycle in which heat energy is converted into mechanical power. By using MATLAB, the pressure and volume diagram of air standard cycles can be plotted and simulated. It is important to understand how to solve for the kinematic equations involved in the air standard cycle, and how to plot the diagram using MATLAB.

This week will cover

• Solving piston kinematics equation to calculate volume trace
• PV diagrams for different operating conditions.
• Thermodynamic relationships
• Pressure-volume variations
• Order of the program
• Plots & legends used in the graphs
• Piston kinematics

Vibrations and dynamics are at the core of physical systems. Most mechanical engineering systems are dynamic in nature. These systems can be represented by equations of motion that form a set of ordinary differential equations (ODEs). It is important for learners to understand how to solve these ODEs, and their application in a real-world context.

This week will cover

• Backward difference formula (BDF) and forward difference formula (FDF) methods to solve ODEs
• Real use of differential equations
• How differential equations relate to real-world applications
• Solving differential equations
• ODE solvers, syntax of ODEs, and various supplementary commands

Curve fitting is used to understand the relationship between different variables by constructing a curve that fits best through a series of data points. Regression analysis identifies the strength of the relationship between two or more variables. This lets engineers understand the relationship between system input and output, as well as predict how the system will behave in the future. Curve fitting and regression can both be done using MATLAB. It is important to understand curve fitting and regression analysis when working with physical systems in MATLAB.

This week will cover

• Polynomials and their best fits
• PolyFit and PolyVal commands
• Calculating errors
• Sum of squares regression (SSR)
• Sum of squares error (SSE)
• Sum of squares total (SST)

The genetic algorithm is based on Charles Darwin’s theory of natural selection in which each step identifies the ‘best’ set of parents to reproduce children. Overtime, the continuous process of doing this yields an optimal population. In the same way, the genetic algorithm can be applied to optimization problems and performed using MATLAB. It is important for learners to understand the genetic algorithm, and how it can be used as an optimization technique.

This week will cover

• Optimization techniques
• Working of the genetic algorithm
• Genetic algorithm syntax and finding the global maxima
• Stalagmite functions and how it works
• Population size, number of generations, fitness value, and termination of further generations