Our design had a motor attached to a slider crank mechanism. This slider is connected to the thrower arm which is connected to a grounded pin element that can slide along the length of the arm. Our analysis was used to find the position of this grounded element based on our desired velocity. We chose to make the crank 6 inches and 15 inches for the coupler. We chose these particular lengths since we wanted to maximize the velocity while mitigating the normal force on the slider. We also had to take into consideration the angle that the coupler would approach the stationary pin. As such we decided to make the coupler 2.5 times as long as the crank in order to reduce the angle and normal force even though this reduces the velocity of the slider. We balance this by making the desired crank angle 90 degrees at the point of release to maximize velocity. Thus, with an rpm of 100 coming from the motor, the velocity of the slider comes out to be 1.6m/s using the instantaneous centers method. We also decided that we wanted the ball to release at a 100 degree angle and 20 m/s. The arm is 21 inches long and the velocity of the release depends on the location of the fixed point along the arm which also acts as an instantaneous center for the arm. Based on this information the distance of the fixed point is the 2.02 inches from the bottom of the arm and 2 inches from the horizontal axis of the slider.
Additionally we did a calculation of the angular velocity needed to produce significant motion of the ball and be visible. By using correlations of the lift force (in this case downward) of a spinning sphere, we would be able to see the downward curving of the ball if thrown at high enough speed and rotation. After analyzing the link lengths, we determined that the ball would have to spin at about 500 rpm, which would be very hard to accomplish unless we used a much smaller spindle. Thus we tried to get as close to this value as possible but because of the very high speed needed, we were unsuccessful.
Slider connecting the slider-crank system to the throwing arm:
