High-density regions within the spiral arms are expected to have profound effects on passing stars. Understanding of the potential effects on the Earth and our Solar System is dependent on a robust model of arm passage dynamics. Using a novel combination of data, we derive a model of the timings of the Solar System through the spiral arms and the relationship to arm tracers such as methanol masers. This reveals that asteroid/comet impacts are significantly clustered near the spiral arms and within specific locations of an average arm structure. The end-Permian and end-Cretaceous extinctions emerge as being located within a small star-formation region in two different arms. The start of the Solar System, greater than 4.5 Ga, occurs in the same region in a third arm. The model complements geo-chemical data in determining the relative importance of extra-Solar events in the diversification and extinction of life on Earth.