As I got to the last part of my recent chair assembly, I decided to try a hunch and redesign my rockers. The rockers on my chairs have always been simply portions of a large circle with an area at the back that has a slightly larger radius. This flatter area at the back of the rockers acts as a brake, slowing the motion and helping it reverse. I have always felt that rockers that are simply a portion of a circle can rock back too far and make me tense.
After years of "winging it", I decided to try laying out a parabola, which naturally and fluidly flattens out toward the ends. After some tinkering with the numbers, I settled on the dimensions and layout shown below.
The layout is pretty simple (and cool!). Start with a baseline that is 38 inches long. Half way across it draw a perpendicular line that is marked at 4 1/8 inches and 8 1/4 inches off the baseline. Next draw lines from the ends of the baseline to the top mark on the perpendicular. Then mark off the sides into equal increments (the more the better). Finally, connect the lowest mark on one side to the highest on the other. Proceed up and down the sides as shown. The lines will form tangents to the parabola and give a relatively smooth curve.
Here is the final rocker, in the chair. I found that by shifting the rockers forward or back, I could place the "brake" exactly where it is most comfortable. I'd be curious to know if anyone else has worked with parabolas this way, and if so, why didn't you tell me!