  In this paper we are interested in BB knots, namely knots and links where the
bridge index equals the braid index. Supported by observations from
experiments, it is conjectured that BB knots possess a special
geometric/physical property (and might even be characterized by it): if the
knot is realized by a (closed) springy metal wire, then the equilibrium state
of the wire is in an almost planar configuration of multiple (overlapping)
circles. In this paper we provide a heuristic explanation to the conjecture and
explore the plausibility of the conjecture numerically. We also identify BB
knots among various knot families. For example, we are able to identify all BB
knots in the family of alternating Montesinos knots, as well as some BB knots
in the family of the non-alternating Montesinos knots, and more generally in
the family of the Conway algebraic knots. The BB knots we identified in the
knot families we considered include all of the 182 one component BB knots with
crossing number up to 12. Furthermore, we show that the number of BB knots with
a given crossing number $n$ grows exponentially with $n$.
