The condition of complete balancing of reciprocating parts of an engine is that the primary force and couple as well as the secondary force and couple polygons must close. Let's understand this in detail:

1. Introduction to reciprocating parts:
Reciprocating parts in an engine include the piston, connecting rod, and crankshaft. These parts undergo reciprocating motion, which creates forces and couples that need to be balanced for smooth and efficient engine operation.

2. Primary force and couple polygons:
The primary force polygon represents the magnitude and direction of the net force acting on the reciprocating parts due to the gas pressure inside the cylinder. Similarly, the primary couple polygon represents the magnitude and direction of the net couple acting on the crankshaft due to the eccentricity of the connecting rod.

3. Secondary force and couple polygons:
The secondary force polygon represents the magnitude and direction of the net force acting on the reciprocating parts due to the inertia forces caused by the reciprocating motion. Likewise, the secondary couple polygon represents the magnitude and direction of the net couple acting on the crankshaft due to the inertia forces.

4. Closing of polygons:
For complete balancing, both the primary and secondary force and couple polygons must close. This means that the vectors representing the forces and couples must form a closed polygon, indicating that the net force and couple acting on the reciprocating parts are balanced.

5. Importance of complete balancing:
Complete balancing of reciprocating parts is crucial to minimize vibrations, reduce wear and tear, and improve the overall performance and efficiency of the engine. Unbalanced forces and couples can lead to excessive vibrations, which can cause fatigue failure of the components and decrease the lifespan of the engine.

6. Balancing techniques:
To achieve complete balancing, various techniques are employed, such as counterweights on the crankshaft, offsetting the crank throws, and using balancing shafts. These techniques help to counteract the unbalanced forces and couples and ensure that the polygons close.

In conclusion, the condition of complete balancing of reciprocating parts in an engine requires the primary force and couple as well as the secondary force and couple polygons to close. This ensures that the net forces and couples acting on the reciprocating parts are balanced, resulting in smoother operation and improved engine performance.