[matthewdenny]

Here is a spreadsheet I made for the throwing arm exit velocity calculations.

You can enter the the radius of the throwing arm, and the motor characteristics, and the angles of the arm when it begins and finishes throwing the ball. Also enter the reduction factor of your motor(Gear boxes and everything combined), the weight of the ball+weight of your throwing arm, and your efficiency (.8 is my starting assumption)

Heres how I set it up:
1)Calculate the force of the vector of the gravity of the ball +arm to overcome
2)Using the torque/speed line for the motor find the torque supplied to the arm at that speed.
3)F=ma, find the acceleration on the ball.
4)assuming the circle is a polygon of n=360 determine the distance needed to travel 1deg of rotation
5) Knowing previous velocity and acceleration and distance, calculate the time to travel the 1 degree
6)Knowing time and distance for this degree, calculate both rotational velocity, and strait line velocity.

Wash rinse and repeat each degree until the release point is reached.

If anyone sees mistakes, or improvements I'd be interested.