Here’s an early post with a chart that shows the 4 original concepts and which measurements are important. The drawings on the chart are just for general reference, they are not to scale. It explains most of the critical relationships between different bars in the linkages.
Here’s my original test drawing of a top mounted design:
And here’s David’s improvement on that design by using cut-outs for chain clearance. Note that the actual lengths of the bars is not critical as long as they clear your router. The critical part is that they are consistent with each other. The distance between the top hole and center hole in the vertical bars must equal the distance between the top and bottom mounting points on the sled AND the distance between the center hole and the chain mounting hole in the vertical bars must equal the distance between the bottom mounting point on the sled and the center of the router bit. The length of the “horizontal” bars will dictate how where that red dotted line is, this is the point that the tip of the chains will trace in space. All 4 horizontal bars must match each other.
And here is my original 45˚ design drawing:
Similar rules apply, parallel bars need to be the same length as each other. Lengthening the pivoting bars will move the red dotted line. Lengthening the two 45˚ bars (the bars that the chains attach to) will buy you more clearance for the router. The chain mounting point does not have to be in the center of the bar, but it must match the distances between the sled mounting points and the router bit (4.5" in this drawing).
Both designs use the same principal of a parallelogram to trace a concentric circle around the router. The biggest mechanical difference between the two is probably that the joints in the top mounted design are under both compression and tension and joints in the 45˚ design are all under tension.