The paper deals with recursive constructions for simple 3-designs based on other 3-designs having $(1, σ)$-resolution. The concept of $(1, σ)$-resolution may be viewed as a generalization of the parallelism for designs. We show the constructions and their applications to produce many previously unknown infinite families of simple 3-designs. We also include a discussion of $(1,σ)$-resolvability of the constructed designs.