Summary of Final Design

One of the first steps in learning how to skateboard is pumping. Pumping is the action which allows the skateboarder to speed up within a half pipe or ramp in order to keep his momentum without touching the ground. Pumping adds energy to the skateboard to replace the energy lost by friction. The pumping action involves the skateboarder “pumping”, or extending, his legs upwards and lifting the upper body. In scientific terms, when the upper body lifts, the center of mass of the skater raises. This raising of the center of mass is what adds energy into the system.

            The physics behind the addition of energy into a system can be modeled after a pendulum. The pendulum path represents a half-pipe and the mass at the end of the pendulum represents the center of mass of the skateboarder. When a skateboarder pumps, he raises his center of mass. In the pendulum model, the raising of mass is analogous to shortening the length of the pendulum. As the length of the pendulum is shortened, the pendulum must accelerate to conserve the angular momentum. This concept can be illustrated by Equation 1, where m is the mass of the pendulum, l the length, g the gravitational constant, θ is the position in radians, and ω is the angular acceleration. When the velocity increases, the energy of the system increases.

mlω² = mgsin(ϴ)       (1)

When the velocity increases, the energy of the system increases. This is a basic concept that can be seen in Equation 2, where v is the velocity of the mass.

 Kinetic Energy = (1/2)mv²     (2)

            Another basic move that skateboarders do is a 180° spin. The skateboarder executes a multi-step process in order to complete the spin successfully.

Step 1) The skateboarder prepares to spin his board, he pre-loads himself by turning his body opposite the spin motion. This is analogous to preloading a spring.

Step 2) He accelerates his upper body in the direction of the spin motion. The friction between the ground and the skateboard prevents the skateboarder’s lower body and the skateboard from  turning due to the reaction torque of the upper body accleration.

Step 3) As skateboard finally leaves the ground, the skateboarder locks his upper and lower bodies together. The momentum from the upper body carries the lower body into the spin. When the skateboarder locks his upper and lower body together, it can be modeled as an inelastic collision of his upper and lower body. For the robot, the principle that is demonstrated is the inelastic collision. During the collision, the velocity of the upper body dictates the speed of the combined masses. 

The following equation shows that the velocity of the top part of the body will travel as as a result of the final velocity of the spin, Vfinal, and the moments of inertias: It for the inertia of the arms, and Ib for the inertia of the body skateboard deck.

  Vtop = Vfinal*(It + Ib)/It 

            The robotic skateboard can perform two tricks. The robot performs pumping through arms which rotate from horizontal to vertical. The arms are weighted on one end and move in unison. When the arms move, they cause the robot’s center of mass to rise. Each arm is actuated by a position controlled gearmotor. The arm structure is attached to another gearmotor in the center of the robot which actuates the spin mechanism. The robot is controlled by an Arduino Uno microcontroller.

In the first two weeks of our project, we constructed a prototype to prove the concept of pumping as well as perform at the Tony Hawk Science event in March 19 2012. The prototype demonstrated how pumping helps to keep momentum in a half-pipe. When pumping, the robot was able complete fifteen oscillations in the half pipe. Without pumping, the robot would only oscillate 7 times before dying out. Although the prototype was not able to sustain pumping or gain height, it proved that the pumping with a robotic skateboard was possible.

Figure 3: First Prototype- Small Model

The final prototype results were very positive. In terms of pumping, the robot was able to not only overcome friction, as the first prototype did, but was able to gain significant height. One trial almost sent the skateboard over the edge of the half pipe. For the spin, the robot was able to perform a 180° spin on the ground. In the half pipe, it successfully performed one spin, then landed to continue moving in the half pipe. All in all, the team successfully created a robot which could demonstrate efficient pumping as well as perform a 180° spin both on the ground and in the air.

Final Design

The Robotic Skateboards functionality can be broken down into two main components.  The first is the pumping apparatus which, by moving mass up and down at the appropriate portions of the half-pipe ramp, allows the skateboard to go progressively higher on the ramp.  The second, spinning component comes into play after the skateboard is consistently going higher than the physical ramp structure.  By spinning the top half of the robot into a physical stop that links the top and the bottom, the entire structure spins 180° and lands back in the half pipe.

Pumping Component:

The pumping mechanism of the robot sits upon the top of a cubic structure holds a “bulk head” which has all major components attached to it. The bulk head

 was machined out of aluminum square plates a ¼ inch thick of various lengths. The two major side plates have attachments in order to bolt and hold the arm lifting motors and gearboxes, and a potentiometer placed at the other end of the motor shaft through the bearings in order to record the position of the arms. The bulk head also contains mechanical stops placed in certain positions in order to avoid the arms hitting the main cubic structure or themselves when rotating. The Motor Drivers were mounted and bolted on top of their respective motors.

                                                                       Figure 1, Motor Placement                                                    Figure 2. Potentiometer Placement

The pumping apparatus on the robot consists of two foot-long arms which attach to dc-brush motors located on the center structure of the robot. The motors are powered by batteries located on the opposite end of the arms. The batteries act as the weight being lifted to change the robots inertia. The dc-motors have 64:1 gearboxes which attach directly to the center structure.

Spin Component: