The BL Lacertae object Mrk 501 belongs to a class of core-dominated radio sources with orthogonal misalignments between the apparent position angles of their radio jets on parsec and kiloparsec scales. New VLBA and MERLIN images of Mrk 501 are analyzed in terms of the geometrical models for such orthogonal jets proposed by Conway & Murphy (1993). Recent hydrodynamical studies by Hardee, Cooper, & Clarke (1994) of the effects of driving helical distortions into a jet by motion of the central engine provide a physical mechanism for generating helically distorted jets with just the properties required by the geometrical model. Applying these hydrodynamical models to Mrk 501 we find that driving periods of a few times 10(4) yr are required to explain the observed morphology. This driving period and the precise jet morphology are consistent with the helical structure being excited by the orbital motion of a binary black hole system. This result, combined with the fact that orthogonally misaligned radio sources comprise approximately half of the total population of core-dominated sources, suggests that binary black holes may exist within 50% of core-dominated sources. For Mrk 501, analysis of the observed jet path, of the VLBA intensity distribution, and of synchrotron/ inverse Compton models for the integrated radio to gamma-ray spectrum provides strong constraints on the physical properties of the jet. Most importantly, the Lorentz factor of the bulk flow must satisfy gamma > 2.1, and the half-opening angle of the helix cone zeta < 12 degrees. These properties and others derived for Mrk 501 are consistent with this BL Lacertae object being a radio galaxy of Fanaroff & Riley (1974) type I (F-R I), whose innermost VLBI regions are viewed at a small angle theta(c) < zeta/(3)(1/2) to the line of sight. For the gamma and zeta limits mentioned above, the simplest relativistic beaming models, with their assumption of a single bulk flow velocity, are inconsistent with the presence of a putative counterjet feature seen on VLBA scales. Such difficulties are avoided by a model, such as that proposed by Laing (1993) for F-R I radio galaxies, which invokes a slower moving shear layer on the surface of the jet.
