The Limaçon of Pascal: Mechanical Generation and Utilization for Fluid Processing

The limaçon of Pascal is a plane curve that possesses some characteristics which qualify it for fluid processing applications. However, the curve has not yet attracted enough attention, neither from industry nor from the mechanical engineering research community, despite the few attempts that have been conducted over the past century. The work presented here is intended to explore various mechanical linkages that can be employed to produce the limaçon and the aspects of these linkages. Mathematical analysis will show that machines based on the limaçon curve possess sinusoidal volumetric relationships and hence, simplified pressure and torque equations can be obtained in closed forms. The concepts discussed here will be demonstrated by using a compressor as a sample application.