Angular positioning device comprising a frame, a first mechanical movement transmission assembly, and a second mechanical movement transmission assembly, the first mechanical assembly comprising: ▪ a first support in pivot connection with the frame, according to a first axis (X 1); ▪ a first connecting rod in pivot connection with the first support, according to a second axis (X 2), which is parallel with the first axis (X 1); ▪ a second connecting rod in pivot connection with the first connecting rod, according to a third axis (X 3), and in pivot connection with the frame according to a fourth axis (X 4), the third and fourth axes being parallel with the first and second axes; and a first actuating device which can rotate the second connecting rod according to the fourth axis (X 4), the second mechanical movement transmission assembly comprising: ▪ a second support in pivot connection with the first support according to a fifth axis (X 5), which is not parallel with the first axis (X 1); ▪ a third connecting rod in pivot connection with the second support according to a seventh axis (X 7), which is parallel with the fifth axis (X 5); ▪ a fourth connecting rod in pivot connection with the third connecting rod according to an eighth axis (X 8), and in pivot connection with the frame according to a ninth axis (X 9), the eighth and ninth axes being parallel with the fifth and seventh axes; and ▪ a second actuating device which can rotate the fourth connecting rod according to the ninth axis (X 9), the angular positioning device being configured such that the fifth axis is parallel with the seventh axis (X 7) in one of the angular positions (α 1, α 2) of the first support around the first axis (X 1) characterized in that the first mechanical movement transmission assembly being configured such that the first support can adopt two distinct angular positions (α 1, α 2) around the first axis (X 1), for each of which the first and second connecting rods generate a dead centre for the first support, in that a third connecting rod in pivot connection with the second support according to a sixth axis (X 6) combined with the first axis, in one of the angular positions of the second support around the fifth axis (X 5), and in that the second mechanical movement transmission assembly being configured such that the second support can adopt two distinct angular positions around the fifth axis (X 5), for each of which the third and fourth connecting rods generate a dead centre for the second support, ▪ a first support in pivot connection with the frame, according to a first axis (X 1); ▪ a first connecting rod in pivot connection with the first support, according to a second axis (X 2), which is parallel with the first axis (X 1); ▪ a second connecting rod in pivot connection with the first connecting rod, according to a third axis (X 3), and in pivot connection with the frame according to a fourth axis (X 4), the third and fourth axes being parallel with the first and second axes; and a first actuating device which can rotate the second connecting rod according to the fourth axis (X 4), ▪ a second support in pivot connection with the first support according to a fifth axis (X 5), which is not parallel with the first axis (X 1); ▪ a third connecting rod in pivot connection with the second support according to a seventh axis (X 7), which is parallel with the fifth axis (X 5); ▪ a fourth connecting rod in pivot connection with the third connecting rod according to an eighth axis (X 8), and in pivot connection with the frame according to a ninth axis (X 9), the eighth and ninth axes being parallel with the fifth and seventh axes; and ▪ a second actuating device which can rotate the fourth connecting rod according to the ninth axis (X 9),