Abstract: Torseur theory is a mathematical tool specially designed for mechanics. Thanks to its unified mechanical description, mathematical generality and operational simplicity, it has significant advantages in modeling, analyzing and computing rigid multibody dynamics: on the one hand, unifying the translation and rotation process in the same mathematical notation; one the other hand, establishing correct physical concepts while making strict mathematical expositions, so that mathematical properties and physical meanings can be well reflected on each other. This paper briefly introduces the research status of spiral theory in mechanics teaching in China and abroad. The mathematical definition of torseur and its mathematical operation properties are presented. The four basic spirals commonly used in theoretical mechanics are expounded, and the spiral descriptions of “fundamental theorems” of vector statics and dynamics are formulated. It is expected that this study can provide new ideas for theoretical mechanics teaching in China.