Reciprocating motion, also called reciprocation, is a repetitive up-and-down or back-and-forth linear

motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and m ...

. It is found in a wide range of mechanisms, including

reciprocating engine A reciprocating engine, also often known as a piston engine, is typically a heat engine that uses one or more reciprocating pistons to convert high temperature and high pressure into a rotating motion. This article describes the common fe ...

s and

pump A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they ...

s. The two opposite motions that comprise a single reciprocation cycle are called

stroke A stroke is a disease, medical condition in which poor cerebral circulation, blood flow to the brain causes cell death. There are two main types of stroke: brain ischemia, ischemic, due to lack of blood flow, and intracranial hemorrhage, hemorr ...

s. A crank can be used to convert into reciprocating motion, or conversely turn reciprocating motion into circular motion. For example, inside an

internal combustion engine An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal co ...

(a type of reciprocating engine), the expansion of burning fuel in the

cylinder A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an ...

s periodically pushes the

piston A piston is a component of reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder and is made gas-t ...

down, which, through the

connecting rod A connecting rod, also called a 'con rod', is the part of a piston engine which connects the piston to the crankshaft. Together with the crank, the connecting rod converts the reciprocating motion of the piston into the rotation of the crank ...

, turns the

crankshaft A crankshaft is a mechanical component used in a piston engine to convert the reciprocating motion into rotational motion. The crankshaft is a rotating shaft containing one or more crankpins, that are driven by the pistons via the connecti ...

. The continuing rotation of the crankshaft drives the piston back up, ready for the next cycle. The piston moves in a reciprocating motion, which is converted into circular motion of the crankshaft, which ultimately propels the vehicle or does other useful work. The reciprocating motion of a pump piston is close to, but different from,

sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often i ...

simple harmonic motion In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the acceleration of the body away from the ...

. Assuming the wheel is driven at a perfect constant rotational velocity, the point on the crankshaft which connects to the connecting rod rotates smoothly at a constant velocity in a circle. Thus, the displacement of that point, is indeed exactly sinusoidal by definition. However, during the cycle, the angle of the connecting rod changes continuously. So, the horizontal displacement of the "far" end of the connecting rod (i.e., connected to the piston) differs slightly from sinusoidal. Circumstances where the wheel is not spinning with perfect constant rotational velocity, such as a steam locomotive starting up from a stop, are very much not sinusoidal. So basically a up and down a repetitive up-and-down or back-and-forth linear motion.

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See also