A design methodology for a Pericyclic mechanical transmission utilizing straight bevel gears has been presented. By virtue of its very high reduction ratio in a single meshing stage, the pericyclic transmission holds promise for significant transmission weight reduction compared to state-of-the-art concepts. Assembly, gear geometry and kinematics of the drivetrain leading to a high reduction ratio while having a very high contact ratio (~8-10 teeth in contact) has been discussed. Tooth contact behavior has been studied in detail. A load distribution model has been developed that can be easily generalized to any internal-external bevel gear mesh. A rolling/ sliding velocity analysis has also been carried out, taking nutational motion into account. This is further used to determine the elastohydrodynamic lubrication characteristics of the meshing gear pairs. The methodology was applied to a conceptual design, resulting in acceptable levels of predicted contact stress and transmission efficiency.