16.2 - Kinematics Analysis
The ideal motion profile for our project is a smooth reduction of the wheel radius (the y-position of the magenta circle in the animation above). We also want a mechanical advantage greater than 1, so that as little force as possible to expand the wheel radius.
This calculation shows that less force is needed to open the wheel as the angle between the wheel and the “ground” shaft increases.
A sketched kinematic diagram for the wheel is shown below. In our analysis, the point of interest is point P which indicates the edge of the wheel. Our wheel requires one degree of freedom. With 4 links and 4 full joints, our calculated mobility is the desired one degree.
The radius of the wheel as a function of the horizontal position of the slider is shown below. As the slider moves away, the wheel shrinks to ~64% of its original radius.
The velocity and acceleration of the wheel were calculated knowing that the servo motor we are using produces a constant angular velocity of 6.16 rad/s when supplied with 6 volts. This means our angular acceleration is 0 rad/s^2.
The wheel’s radius does not have a linear relationship with the slider position, which must be taken into account as we actuate the wheel radius adjustments. There is also minimum acceleration of the wheel slat when the slider distance is approximately 43 mm from the gear box.