Parallelepiped

Parallelepiped is a solid figure, all of whose six sides are parallelograms, from which it follows that its edges consist of three sets of four parallel lines. Its three diagonals - the lines joining opposite corners of the figure - meet at a point and mutually bisect each other. The most commonly occurring form of parallelepiped is bounded by rectangular parallelograms, and is exemplified by an ordinary cigar-box; this is called a rectangular parallelepiped. Among crystals are found numerous examples of different parallelepipeds, calc spar, for instance, occurs naturally in that form of it which is known as a rhombohedron. When all the faces are squares, the parallelepiped becomes a cube. Parallel Motion was invented by Watt as part of his steam engine. In a beam engine the end of the beam moves in a circular path, while the piston-rod, whose motion must be transmitted to it, moves in a straight line. If the beam and piston-rod were connected by a single link, the horizontal component of the circular motion of the former would produce great pressure on the stuffing box, and tend to bend the piston-rod. To overcome this, Watt connected the beam and piston-rod by three links pivoted together and to the beam, making a parallelogram of which one side was a portion of the beam, the piston rod being pivoted to one corner. By the addition of a "radius rod" pivoted to the lower corner of the parallelogram, and also to a fixed point on the framework of the engine, and by properly proportioning the lengths of the links, the piston rod can be constrained to move in a straight line. Various parallel motions have been designed to suit different patterns of engines; but, as the beam engine is now practically obsolete, they are no longer required. Parallel motions are, however, used in some pieces of mechanism, such as the steam-engine indicator.