# Screw Theory for Robotics as the best mathematics for Mechanics!

Today is the International Day of Mathematics (IDM), being a worldwide celebration.

Let us take advantage to recall the importance of screw theory in robotics is recognized, but in practice, not many teach it to engineering students. Therefore, only a few postgraduates know how to exploit it. However, in various areas of robotics, the methods and formalisms based on the geometry and algebra of the screws have proven superior to other techniques and have led to significant advances. It is essential to communicate and disseminate these methodologies among as many students as possible who might be working with robots in the future.

The screw theory geometric description best captures the most salient physical features of a robot. However, these screw theory tools inaccessible to many students require a new language (e.g., screws, twists, wrenches, adjoint transformation, geometric Jacobian, spatial vector algebra). The rules for the manipulation of this language can seem kind of obscure. In fact, at the heart of the screw theory, there is a high-level but straightforward geometric interpretation of mechanics. The alternative is the most standard algebraic alternatives, which unfortunately make us often buried in the calculation details.

The key advantage of using screw theory comes from the 6D vector representation, in which the linear and angular aspects of motion work combined into a unified set of equations.

This blog design intends to build a functional bridge between the mathematical fundamentals, which are extensive, and the practical technological robotic applications.