This paper broadly discusses aspects of the novel Rotary Vane Engine (RVE). It also considers, in detail, the geometrical structure of work unit and the entire engine. The rigorous mathematical description of work unit and torque transmission mechanism are presented for a first time in literature. Although the RVE is a simple structure possessing a small number of moving parts, it is this property that provides the RVE with an important advantage when compared to a usual reciprocating engine. The main idea is to use noncircular gears in torque transmission mechanism together with Kauertz-Virmel work unit. It is found that the rotary engine can produce almost constant angular velocity of the flywheel, which would result in an efficient and smooth performance.