Elliptical Trainer Modeling
- Author:
- John Golden
- Topic:
- Trigonometry
Elliptical Trainers seem to be misnamed. Many of them are a linkage of a circular wheel to a horizontal bar, with the pedal fixed on the rod.
Can you find a sinusoidal model for the pedal's height and another for it's horizontal position?
Can the height and horizontal position still be modeled with trigonometric functions even though the path is not circular?
a) What are reasonable values for the length of the rod and diameter of the wheel?
b) Which point in the left graph represents the height and which the horizontal position? Find a function to model both as well as you can. How is the fit?
c) Can you relate the values in your functions to the radius and position of the wheel and the length of the rod/position of the pedal?