This paper examines the mechanical efficiency of reciprocating heat engines in a general setting. From an abstract mathematical characterization of machines, the relation of the pressure-volume cycle of an engine and the characteristics of its mechanism to its useful work output is established. Using the ideal Stirling engine in conjunction with this relation, a functional upper bound on the mechanical efficiency of all engines is derived. This shows the existence of limits on compression ratio under conditions relating the level of performance of the mechanism to the ratio of engine operating temperatures. This has implications for the design of engines intended for operation from low grade sources, such as industrial waste heat or passive solar energy.