A swashplate is a device used in mechanical engineering

Mechanical engineering

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the...

 to translate the motion of a rotating shaft into reciprocating motion

Reciprocating motion

Reciprocating motion, also called reciprocation, is a repetitive up-and-down or back-and-forth motion. It is found in a wide range of mechanisms, including reciprocating engines and pumps. The two opposite motions that comprise a single reciprocation cycle are called strokes...

, or to translate a reciprocating motion into a rotating one to replace the crankshaft

Crankshaft

The crankshaft, sometimes casually abbreviated to crank, is the part of an engine which translates reciprocating linear piston motion into rotation...

 in engine designs.
A swashplate consists of a disk attached to a shaft. If the disk is aligned squarely on the shaft then rotation of the shaft will turn the disk with it and no swashplate effect will be seen. Even a slight displacement of the disk from the square position, however, will cause the disk edge to appear to describe an oscillating linear path when viewed from a non-rotating point of view away from the shaft.