Prototype and Iterations:

Our initial prototype, shown in Figure 1 below, is a four-bar linkage with about 60 degrees between our two ground links. The end effector has a spoon attached to the fourth link to replicate the hand/cradle the basketball will be placed into for the final prototype. Using link 2 as the driven link we were able to create a good launch arch and escape velocity, proving to us that we'd be able to refine the linkages to have less play and be able to create a consistent shot into a basketball hoop with the use of a motor.

Figure 1: Initial Prototype

We initially wanted to use a quick return mechanism, pictured in Figure 2 below, due to it quickly building up velocity, creating a better shot. However after comparing it to a four-bar mechanism, like Figure 3 below, we realized that that four-bar would be better. This is due to the four-bar having rotational bearings that are better than prismatic bearings because prismatic bearings would have to fight more friction than rotational bearings. The slotted mechanism on the quick return would also have less mechanical advantage than the four-bar, leading to a better escape velocity on the four-bar mechanism.

Figure 2: Quick Return Mechanism

Figure 3: Four Bar Mechanism

Kinematic Analysis:

Mobility Calculations

M=3(L-1)-2(J₁)

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

Our system has one degree of freedom

Force Analysis of Link 4

r_in= 1.5207 in

r_out= 3 in

w₂=600 deg/s (motor)

w₄= 558 deg/s

Mechanical Advantage=(F_out/F_in)=(w₂/w₄)*(r_in/r_out)

m_a= .545

Kinematic Analysis of Link 4

Position Analysis

The two images below depict our mechanism at its toggle points. The arc shows the path of the launcher through the full range of motion.

Figure 4: Position Analysis

Velocity Analysis

The animation below shows the linear X-velocity (top graph) and Y-velocity (bottom graph) of the launch point during the mechanisms cycle.
The X-velocity nears its peak close to the ball's launch point.

Figure 5: Velocity Analysis

Acceleration Analysis

The system is pictured below at the launch point's maximum linear acceleration. This will be the angle from which the ball will be launched.
The angle is just before the toggle point when bar 4 begins to return along its arc. This is ideal for minimizing redundant motion.

Figure 6: Acceleration Analysis

Bill of Materials:

Electronic Components:

100RPM 12V Motor
Arduino
L298N Motor Driver
12V Power Supply
Servo Motor
Jumper Wires

Laser Cut Components:

4 Linkages
Base Plane
Spacers

3D-Printed Components:

Basketball
Net
Lock collars

Stock Components:

Bearings
Axles
Nuts
Bolts
Washers

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