Paul D Jose back in April 1965 published a ground breaking paper titled the "Sun's Motion and Sunspots*"
The path of the Sun around the SSB was plotted along with crude angular momentum (AM) graphs that even today show the somewhat obscure AM perturbations made clear in Carl's 2007 graph. Jose was a true pioneer in planetary theory that I believe deserves the naming rights for the current predicted solar grand minimum. One of the main principles of his paper was the recurring 178.8 year cycle of the 4 gas giants that he postulated returned to the same position. This cycle has been used in multiple papers along with a great deal of internet literature especially those consumed with numerology.
My research suggests the 178.8 year cycle of the gas giants is non-existent once tested over multiple cycles. In fact it barely lasts even one cycle when looking at the natural progression of the outer 4 planets. When looking at AM theory the moving planet positions and that variability is what drives the shape of the Holocene solar proxy record. In reality the outer 4 planets which are responsible for the solar path around the SSB that never returns to the same position, but there is a rough cycle of 4628 years where we get pretty close. 4628 is 27 x 171.4 (Uranus/Neptune synodic) and although there is a gradual precession by Jupiter over thousands of years the pattern is reasonably tight.
In the following diagrams the 178.8 cycle is shown to disappear very quickly, but the 4628 cycle is certainly more robust.
Click on the images for a full size view.
179 year progression.
4628 year progression.
The 4628 year cycle shows a main movement of Jupiter, but this movement does have a significant effect on the strength and overall AMP patterns. Over the 4628 year period Jupiter goes through 390.24 orbits. Saturn over the same time period experiences 157.11 orbits.