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BMW filed a patent showing its approach to variable compression ratio. While Nissan's idea uses a mechanical linkage to adjust the piston, BMW's idea uses a ring gear along the crankshaft, connected to the pin of one of the pistons. Rotating the outer ring gear adjusts the piston's movement, increasing or decreasing the compression ratio. Because the ring gear and the internal adjusting gears takes up the same space as the crankshaft, the system is theoretically more compact than Nissan's.

Here's what the abstract says:
"The invention relates to a device (10) for varying a compression ratio of a reciprocating-piston internal combustion engine (100), having an externally toothed eccentric (3) which is designed to be arranged between a crankpin (28) of a crankshaft (20) of a crank drive (20') and a connecting-rod eye of a connecting rod (22) in rotationally movable fashion for the purposes of varying a stroke length of a piston, which is mechanically coupled to the connecting rod (22), of the reciprocating-piston internal combustion engine (100), having an adjusting unit (12) which is mechanically coupled to an external toothing (3-1) of the eccentric (3) and which is designed for adjusting the eccentric (3) by rotation of the eccentric (3), and having a coupling unit (56) which is designed for mechanically coupling the eccentric (3) to the adjusting unit (12) and which, for this purpose, is formed with first and second pick-off shafts (5, 6) which are arranged parallel to one another, radially spaced apart from one another and mechanically coupled to one another, wherein the first pick-off shaft (5) is mechanically coupled to the external toothing (3-1) of the eccentric (3) and the second pick-off shaft (6) is mechanically coupled to the adjusting unit (12), and wherein the coupling unit (56) and in particular the first and second pick-off shafts (5, 6), the eccentric (3) and/or the adjusting unit (12) are designed for being partially or entirely arranged (a) in the interior of the crankshaft housing of the crankshaft (20), (b) within a structural space of a web (23) of the crankshaft (20), and/or (c) within a structural space of a counterweight (24)."

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