An analysis of the Bricard linkages

Abstract Mobile overconstrained loops are now familiar to linkage kinematicians, but 50 years ago they posed a puzzle to the few who studied the motions of jointed rigid bodies. Ranking high in significance among the “paradoxical” linkages is the group due to Bricard, from the first quarter of this century. Unfortunately, these 6-revolute loops, of considerable interest to line geometricians, have been subject to a great deal of misunderstanding, and have never been delineated by appropriate sets of independent closure equations. This paper is an overdue attempt to remedy the situation.