Leg Press Geometry
A wonderful geometry problem from the weight room. Linear measurements are in inches. Some questions:
- As posted in the image: What is the difference between the value of ß when the seatback is in the "high" (or less-reclined) position and the value of ß when the seatback is in the "low" (or more-reclined) position?
- At some moment between the "high" and "low" extremes of the seatback, ß reaches its minimum value. What is this minimum value of ß? What is the corresponding value of α at that moment?
- If you wanted to preserve the range of α but increase the difference of ß between the "high" and "low" seatback positions by 5°, which linkage length(s) would you change? What might the new value(s) be?
- Other than the geometry displayed here, what other real-world considerations would you have to ponder when designing such exercise equipment?
- What are the advantages of using CAD or geometry software such as GeoGebra to address such questions? What are the advantages of taking an analytic approach with the pencil-and-paper Math skills you learn in Geometry/Trigonometry/PreCalculus class?
- What other good questions have I neglected to ask here?