T₁-Positions of Four-bar Linkages

This paper deals with the hitherto unexplored problem of determining the T₁-positions of the first-kind of the coupler link for all types of 4R four-bar linkages. Geometrical proofs for the existence and number of T₁-positions are given based on geometrical inequalities. The number of T₁-positions are enumerated for each circuit and branch of all types of linkages. Analytical as well as geometric methods for the determination of the configuration of the linkage at an asymptotic configuration are also presented. T₁-positions of 3R1P four-bar linkage are also discussed.