A two-mass model with a spring and a damper in the vertical direction, accounting for vertical translational motion and a torsional spring and a damper connecting the rotational motion of two masses is used to simulate the dynamics of a tennis ball as it comes into contact with a flat surface. The model is supposed to behave as a rigid body in the horizontal direction. The model is used to predict contact of the ball with the ground and applies from start of contact to end of contact. The springs and dampers for both the vertical and the rotational direction are linear. Differential equations of motion for the two-mass system are formulated in a plane. Two scenarios of contact are considered: Slip and no-slip. In the slip case, Coulomb??s law relates the tangential contact force acting on the outer mass with the normal contact force, whereas in the no-slip case, a kinematic constraint relates the horizontal coordinate of the center of mass of the system with the rotational coordinate of the outer mass. Incorporating these constraints in the differential equations of motion and applying initial conditions, the equations are solved for kinematics and kinetics of these two different scenarios by application of the methods for the solutions of second-order linear differential equations. Experimental data for incidence and rebound kinematics of the tennis ball with incidence zero spin, topspin and backspin is available. The incidence angles in the data range from 17 degrees up to 70 degrees. Simulations using the developed equations are performed and for some specific ratios of inner and outer mass and mass moments of inertia, along with the spring-damper coefficients, theoretical predictions for the kinematics of rebound agree well with the experimental data. In many cases of incidence, the simulations predict transition from sliding to rolling during the contact, which is in accordance with the results obtained from available experimental measurements conducted on tennis balls. Thus the two-mass model provides a satisfactory approximation of the tennis ball dynamics during contact.

A two-mass model with a spring and a damper in the vertical direction, accounting for vertical translational motion and a torsional spring and a damper connecting the rotational motion of two masses is used to simulate the dynamics of a tennis ball as it comes into contact with a flat surface. The model is supposed to behave as a rigid body in the horizontal direction. The model is used to predict contact of the ball with the ground and applies from start of contact to end of contact. The springs and dampers for both the vertical and the rotational direction are linear. Differential equations of motion for the two-mass system are formulated in a plane. Two scenarios of contact are considered: Slip and no-slip. In the slip case, Coulomb??s law relates the tangential contact force acting on the outer mass with the normal contact force, whereas in the no-slip case, a kinematic constraint relates the horizontal coordinate of the center of mass of the system with the rotational coordinate of the outer mass. Incorporating these constraints in the differential equations of motion and applying initial conditions, the equations are solved for kinematics and kinetics of these two different scenarios by application of the methods for the solutions of second-order linear differential equations. Experimental data for incidence and rebound kinematics of the tennis ball with incidence zero spin, topspin and backspin is available. The incidence angles in the data range from 17 degrees up to 70 degrees. Simulations using the developed equations are performed and for some specific ratios of inner and outer mass and mass moments of inertia, along with the spring-damper coefficients, theoretical predictions for the kinematics of rebound agree well with the experimental data. In many cases of incidence, the simulations predict transition from sliding to rolling during the contact, which is in accordance with the results obtained from available experimental measurements conducted on tennis balls. Thus the two-mass model provides a satisfactory approximation of the tennis ball dynamics during contact.

With the increasing popularity of phone application development, a number of features have surfaced that enable users to utilize extended functionalities with their phone. With a single device, a user is now able to have access to the latest trends. As a result, functionalities from various products such as personal computers or GPS devices can now be accessible in one place. While this technology is evolving at a fast rate, it is the embedded technology and hardware that drive it which facilitate the innovative designs and solutions. At the other end of the spectrum of embedded systems, companies continue to maintain legacy products that use embedded chips programmed through their flash memory. With this perceived commitment to stay loyal to their older product designs, it has become rather cumbersome for such companies to stay current with the latest hardware and software trends. The result is higher costs to the customers for their high-end products. While the average user invests in newer and faster Google phones or iPhones, it is unlikely that the same can be said for commercial products such as a refrigerator or a ball machine. What if a development framework existed that allowed customers to have access to better user interfaces and functionalities over the lifetime of their product? In this Masters report, an innovative approach is discussed which demonstrates the latest mobile phone technology combined with an existing embedded device being applied to the conversion of a low-end tennis ball machine into an affordable high-end one. / text