Balance (biomechanics) – an ability to maintain the line of gravity (vertical line from center of mass) of a body within the base of support with minimal postural sway. Sway is the horizontal movement of the center of gravity even when a person or object is standing still.

• Balancing machine – a measuring tool used for balancing rotating machine parts such as rotors for electric motors, fans, turbines, disc brakes, disc drives, propellers and pumps
• Your cell phone is able to vibrate because there’s a little motor inside that rotates a small, off-balance weight.
• Balancing boy equilibrium toy – demonstrates stable equilibrium, from 1905 German scientific equipment catalog. The device consists of two pieces, the balancing figure on tiptoe, and the stand that supports it. It appears that the figure’s center of gravity is above the stand, so it should fall over, but if tilted it rights itself, rocking back and forth. In actuality because of the two metal ball weights attached, the figure’s center of gravity is located below its support point, under the surface of the stand. Therefore tilting the figure raises the center of gravity, increasing the potential energy, so it is in stable mechanical equilibrium.

What’s the problem?
The Cubli (video 2:37) is a 15 × 15 × 15 cm cube that can jump up and balance on its corner. Reaction wheels mounted on three faces of the cube rotate at high angular velocities and then brake suddenly, causing the Cubli to jump up. Once the Cubli has almost reached the corner stand up position, controlled motor torques are applied to make it balance on its corner. In addition to balancing, the motor torques can also be used to achieve a controlled fall such that the Cubli can be commanded to fall in any arbitrary direction. Combining these three abilities — jumping up, balancing, and controlled falling — the Cubli is able to ‘walk’.

• Ask – Machines are able to mimic many human skills. Understanding how to replicate these skills is important to putting machines to work. Balance and using shifting balance for locomotion is an interesting example. How can a cube move to a position so it is balancing on one of its corners?
• Imagine – Gyroscopes are frequently used for balancing kids’ toy tops and satellites, but they usually have to have help to get to their balance position. How can this idea be expanded so the cube can start from lying on a flat side?
• Plan, Create – In order to be useful, the cube needs to be able to start from any side and balance on any of its corners. How can this be achieved within the cube?
• Improve – How can the balancing ability be used as part of locomotion? What sequence of actions are required to move from one place to another?

That’s engineering

• velocity – a measure of how fast something has moved in a particular direction. In physics, velocity means the time it took an object to move from one place to another (displacement), and the direction of movement
• center of gravity – the point where an object can be balanced perfectly by a sharp point holding it up under the object. It is the center of mass acting in a gravitational field.

Engineering ideas

• angular velocity, motor torque, reaction wheels, flywheels, motors, sensors, equilibrium, directional information, gravitational acceleration, linear acceleration, angular acceleration, pressure, spatial orientation, support

Do It
Challenges for you to work on…

• Balancing Act – interactive simulation
• Find objects with gyroscopes as part of their design.