2.4 Kinematic Analysis

Mobility Calculations: 

M=3(L-1)-2(J₁)

M=3(4-1)-2(4)=1

Our system has one degree of freedom

Figure 1: Four-bar shooting mechanism showing links and joints in motion

We mainly wanted to calculate the shooting distance and velocity of the ball as it's released so we focused our kinematic analysis on two aspects, the position and velocity of both the input link 2 and the end effector. We also calculated the trajectory of the ball ensuring that it would land at our desired locations (close three, half court, far three, and full court).  To accurately calculate everything we needed to complete this project we first needed to determine link lengths and the angle of the system along with what speed the motor should rotate at. We then applied basic four-bar and vector loop equations to conduct our analysis of position and velocity, using the values shown below. The results of these calculations are shown in Figures 2 through 4 below. Using the output velocity found we were able to predict the trajectory of the ball at different input speeds, shown in Figure 5, using simple projectile motion equations.

Link 1= 3.4 in

Link 2= 1.5 in

Link 3= 5.5 in

Link 4= 4.5 in

End Effector = 11.93 in

Angular Offset= 60.28 degrees 

Figure 2:  Omega out/omega in vs input link angle  

Figure 3:  Output link angle vs input link angle 

Figure 4:  Center point of the end effector from ground link 4

Figure 5: Theoretical projectile motion for targets based on different input motor speed