8.2 Project Prototype
Kinematic Analysis
The goal of this mechanism is to capture the complex motion of a person bowling a ball to score a strike. In order to do so, various variables must be taken into consideration and fine tuned to truly replicate the necessary motion. For example, we must consider the path, velocity, acceleration, and force on the ball as it’s released. With all this in mind, our team has chosen a particular geometry coupled with kinematic analysis to achieve our goal for this mechanism. A sketch of this mechanism is shown below.
Figure 1: Sketch of Bowling Mechanism
L1 is the ground link that will attach the mechanism to the frame of the entire system, keeping it stable and in place. L2 is the driving link that will be rotated around the origin point at a constant angular velocity that we currently have set at 3.14 rad/s. Point P is where we will attach the bowling ball holder, which in this case is simply a marble. To visualize this, an animation of the mechanism is shown below
Figure 2: Animation of Bowling Mechanism w/ Velocities
The above animation represents a desirable motion for our mechanism. Point P, where the marble will sit, has an arc-like motion during its points of highest acceleration. This is similar to that of a human swinging the bowling ball from behind them to release it in front in order to generate the proper amount of force. With this motion in mind, we then have to look at Point P’s numerical position, velocity, and acceleration to tweak any necessary lengths, angles, or rotational velocities to achieve an even better motion profile. We can also use this data to determine when the release of the bowling ball will occur at point P. We would want this to occur at a time where the acceleration during the release of the ball is significant enough to overcome the friction of the bowling alley floor and knock down the pins at the end.
Figure 3: Bowling Mechanism Mobility Calculations (Gruebler and Grashof)
Figure 4: Path of Point P
Figure 5: Graph of Velocity of Point P vs. Angle of L2
Figure 6: Graph of Acceleration of Point P vs. Angle of L2
Looking at Figure 4, we want to release the marble somewhere in between that 2-3 inch mark on the x-axis in order to get a more parallel velocity and acceleration in relation to the bowling alley floor. After all, we want the ball to move forward, not up or down. Using this target position and the animation in Figure 2, we can estimate that the angle of the input link is somewhere around 15 degrees when Point P reaches that 2-3 inch mark. This lines up with a velocity of 3 in/s and an acceleration of 40 in/s^2, looking at Figures 5 and 6, respectively. With these values, we can now perform some force calculations to see if the ball will travel the distance and topple over the 3D printed bowling pins at the end of the bowling alley.
Figure 7: Force Calculations after Marble is Released
From the initial acceleration of the marble after it is released we can calculate the initial force of the marble. We can then use the weight of the marble alongside a friction coefficient between steel and wood to calculate the frictional force on the marble. When both are found you can then calculate the final force of the marble on the pins. However, with our current setup, the marble will not be able to overcome the force of friction and will end up stopping early. This estimate is conservative so even if it happens to overcome the force of friction, the force will end up being too low. As a result, we will have to go back and adjust the angular velocity of the input link to increase the acceleration and velocity of the marble as it’s released to achieve a higher output force of the ball on the pins.
Final Design Considerations
For our final design, our top priority is to change up the input link angular velocity to achieve the necessary force on the ball in order to topple the pins. This is an essential part of our project and is top priority. Aside from this, we can also fidget around with the link lengths of L2 and L4 in order to achieve a flatter arc as the ball is released. This will help get a better release point, which in turn will help maximize the acceleration and velocity we can achieve.
Iteration Document
Bill of Materials
Metal marble (heavier to decrease bouncing and have more inertia)
12V DC motor
Axel Collar for motor to crank (Driving link)
3mm Bearings
3mm Axles (buy these online)
6mm Acrylic
Release Mechanism:
Rubberbands
Strings
3D Printed hand/bucket