Kempe's (focal) linkage generalized, particularly in connection with Hart's second straight-line mechanism☆

Abstract Very few kinematicians are aware of the existence of the focal linkage, which is an overconstrained one. Since there are many applications that could be derived from the linkage or from its derivatives, a thorough investigation has been made into the properties of the focal linkage. Here, a geometric approach as well as an algebraic one clears up some of the mystery that hangs around the mechanism. One of the main results that is achieved in the paper is the invention of a new eight-bar linkage containing a bar having rectilinear translation.