Timeline of alignments (1805-1993)
The big picture: visualising how three cycles fit in a single timeline
The synodic cycles of the giant planets have a common periodicity of 179 to 180 years. This suggests that a timeframe of 180 years is the most relevant to draw a comprehensive timeline of their alignments. The "big cycle" that covers most of the 19th and 20th centuries started around the time of the Saturn-Uranus conjunction of 1805 and the Saturn-Neptune conjunction of 1809, before the Uranus-Neptune conjunction of 1821. It ended after the Saturn-Uranus-Neptune stellium of 1988-89, with the Uranus-Neptune conjunction of 1993.
The circular timeline below shows how four Saturn-Uranus cycles (1805-1988), five Saturn-Neptune cycles (1809-1989) and one Uranus-Neptune cycle (1821-1993) fit into a timeframe of about 180 years.
An approach to build a timeline of the "big cycle"
Based on this observation, I've used the following approach to build the timeline presented below:
Add the hard alignments in the Uranus-Neptune cycle;
Look for Saturn hard alignments with Uranus and Neptune that highlight those alignments, such as a stellium, a double square or a T-square.
Look for Jupiter hard alignments that further highlight the alignements above;
Add the conjunctions in the Saturn-Uranus and the Saturn-Neptune cycles;
Look for Jupiter hard alignments that highlight those conjunctions, such as a stellium, a double square or a T-square.
A timeline focused on the cycles between Saturn, Uranus and Neptune (1805-1993)
The approach described above leads to the following timeline:
1805: Saturn-Uranus conjunction
1809: Saturn-Neptune conjunction
1821: Uranus-Neptune conjunction, highlighted from mid-1818 to early 1820 by Saturn's squares with Uranus and Neptune.
1846: Saturn-Neptune conjunction
1852: Saturn-Uranus conjunction
1868-70: Uranus-Neptune square, highlighted in 1872 by Saturn forming a T-square with Uranus and Neptune, and further highlighted by the Jupiter-Uranus conjunction of June 1872.
1882: Saturn-Neptune conjunction
1897: Saturn-Uranus conjunction, highlighted by a stellium of Jupiter, Saturn and Uranus (within 20 degrees) from Oct 1900 to Nov 1901.
1906-10: Uranus-Neptune oppositions, highlighted in 1909 by Saturn forming a T-square with Uranus and Neptune, and further highlighted in Nov 1910 by a Jupiter-Saturn-Uranus wide T-square.
1917: Saturn-Neptune conjunction
1942: Saturn-Uranus conjunction, highlighted by a stellium of Jupiter, Saturn and Uranus (within 7 degrees) from Feb to May 1941.
1952: Saturn-Neptune conjunction, highlighted by a Jupiter-Saturn-Uranus T-square in Feb 1952.
1954-56: Uranus-Neptune square, highlighted by a Jupiter-Uranus conjunction from Oct 1954 to May 1955, and further highlighted in 1956-57 by Saturn trine Uranus.
1988: Saturn-Uranus conjunction
1989: Saturn-Neptune conjunction
1993: Uranus-Neptune conjunction, highlighted in 1988-89 by Saturn forming a stellium with Uranus and Neptune, and further hightlighted by the Jupiter oppositions to Saturn, Uranus and Neptune from Aug 1989 to June 1990.