3. Kinematics

1. Introduction     2. Design Considerations     4. Prototyping & Building     5. Results & Discussion

To determine how I could use gears to reach the desired fan RPM, I performed a kinematic analysis. First, I calculated the input speed (equ. 1). The contact cylinder on the bike trainer has a radius r of 1".  I assumed that there was no slip between the bike tire and surface of the cylinder and that the wheel was rotating at a linear equivalent of 15 mph.

 equ. 1

I wanted the input rotation to drive a four-bar mechanism that would transfer movement between the rear wheel and the location where the rider is seated. However, with the tools and materials I have at home, I cannot accurately build a four-bar that could move at that high speed safely and without breaking. I calculated that at at that input speed, some points on the four-bar would move at approximately 70 mph. Moreover, most velocity values in our homework problems were a at least an order of magnitude lower, so 2500 rpm did not seem like an appropriate input speed. I wanted to reduce the rpm to a more reasonable speed of less than 100 rpm. 

Due to the limited number of available gears, I planned to reduce the speed in three stages. In the first stage, a bike gear with a radius of 4 cm would drivesa second bike gear with a radius of 9.5 cm using a chain. Thus, the speed is reduced by a factor of 2.375 to 1060 rpm. The larger bike gear drives a shaft that spins a lawnmower gear with a radius of 1.5 cm. The smaller lawnmower gear will drive a larger lawnmower wheel with a radius of 7.5 cm. This gear ratio will reduce the speed again by a factor of 5 to 212 rpm. However, this speed is still too fast for driving the four-bar mechanism, so another pair of lawnmower gears will reduce the speed again by factor of 5 to 42 rpm. Now that the four-bar can safely transfer the rotational motion to where the rider is seated, the speed must be increased up to about 500 - 800 rpm, or the speed of a typical box fan. This velocity increase is accomplished by two pairs of Roomba gears with diameters of 1.25 and 0.375” and 1 and 0.25”, respectively. These gears increase the velocity by a combined factor of 12.33 for a final velocity of 565 rpm.

The output rotational velocity of the fan can be expressed as a function of the bike velocity:

As the rider pedals as speeds of 12 to 22 mph, the velocity of the fan increases within the range of a typical fan (Fig. 1).

Figure 1: As the bike speed increases, fan speed increases linearly.

A schematic of the proposed system is summarized below (Fig. 2)

Figure 2: A schematic of the proposed gear train with rotational velocities of each component labeled for an input speed of 15 mph.

1. Introduction     2. Design Considerations     4. Prototyping & Building     5. Results & Discussion