Abstract
Goldberg's investigation of 8-bar multiloop spatial linkages, and extension of his innovative study of 5- and 6-bar loops, was inspired by the much earlier research of Kempe into multiloop planar chains. Goldberg regarded his solutions as analogues of Kempe's, but severe limitations have been found to apply to the corresponding cases. A series of latter-day papers has systematically examined some of Kempe's findings and several related matters. In particular, the almost comprehensive work on the “star-point” linkages has allowed us far greater insight into various aspects of Kempe's discoverings and the results of those who followed him. Here, we are able to determine the true analogues of Goldberg's linkages, complete the analysis of the star-point chains, further clarify Darboux's exposition on the subject and announce a new linkage.
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