This paper concerns a mechanics of interactions of helical structures in proteins. Helices are the most important secondary structures of proteins and contribute the formation of a more complex 3-D structure, and so the analysis of interactions of helices is quite critical. We examine 1290 protein structures that have 2.0 Å or better resolutions and less than 20 percent of their sequences in common. Interactions between helices are represented by two parameters: the distance and angle. Assuming that helices are slender rigid rods with finite length, we define three different mechanisms of interactions: (1) line-on-line contact; (2) endpoint-to-line contact; and (3) endpointto- endpoint contact. In this paper, interactions for the first case are expressed with the 3-D relative rigid-body motion (position and orientation) and the unique volume element for correctly integrating over rigid-body motions are determined using six parameters. The results are extremely useful for the correct analysis of interactions in terms of distance and angle without the statistical biases inherent in the three data sets.