Robert's Linkage

This linkage by Richard Roberts represents the most general "four bar" linkage. The point P is on the middle link BC, but offset from it. Here the 4th bar is the link AD, which is also the fixed base.

Notice that with these particular measurements the point P is very close indeed to the straight line between AD.

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The complete locus is rather complex, since from a mathematical point of view the linkage could be fliped down, and the point P could be independently flipped up, giving four branches to the locus.

Chris Sangwin, 19 Jan 2007, Created with GeoGebra