Biarc analysis for skinning of circles

By circle skinning we have a discrete set of circles and we would like to find two curves, which touch each of them and satisfy some conditions. There exist methods to give a solution for this problem, but none of them use biarcs for the construction. Meek and Walton published a very deep analysis of biarcs in [1], and they divided them into several families. Of course one of the basic problems is to find the mentioned curves for two circles. In this paper several necessary conditions are given to avoid intersections in this basic case between the skinning curve and the circles using a concrete family of biarcs from [1]. A method is publicated in [3] with which we can find the touching points for the skinning