On the classification of a large set of rational 3-tangle diagrams

We note that a rational $3$-tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational $3$-tangle diagrams up to isotopy. However, there is no perfect classification about rational $3$-tangle diagrams such as the classification of rational $2$-tangle diagrams corresponding to rational numbers. In this paper, we classify a large set of rational $3$-tangles which are generated by only three generators.