The Cubli 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’.

Lead Researchers: Gajamohan Mohanarajah and Raffaello D’Andrea

This work was done at the Institute for Dynamic Systems and Control, ETH Zurich, Switzerland and was funded in part by the Swiss National Science Foundation (SNSF), grant number 146717.

Resources

http://www.idsc.ethz.ch/Research_DAndrea/Cubli

http://robohub.org/swiss-robots-cubli-a-cube-that-can-jump-up-balance-and-walk-across-your-desk/

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Moving an object up an inclined plane requires less force than lifting it straight up, at a cost of an increase in the distance moved. The mechanical advantage of an inclined plane, the factor by which the force is reduced, is equal to the ratio of the length of the sloped surface to the height it spans. Due to conservation of energy, the same amount of mechanical energy (work) is required to lift a given object by a given vertical distance, disregarding losses from friction, but the inclined plane allows the same work to be done with a smaller force exerted over a greater distance.

The angle of friction, also sometimes called the angle of repose,is the maximum angle at which a load can rest motionless on an inclined plane due to friction, without sliding down. This angle is equal to the arctangent of the coefficient of static friction μ_s between the surfaces.

Inclined Plane Example

The inclined plane, shown in Fig. , has an incline length l (AB) = 8 ft and a height h (BC) = 3 ft. The inclined plane permits a smaller force to raise a given weight than if it were lifted directly from the ground.

For example, if a weight W of 1000 lb is to be raised vertically through a height BC of 3 ft without using an inclined plane, a force F of 1000 lb must be exerted over that height. However, with an inclined plane, the weight is moved over the longer distance of 8 ft, but a force F of only 3/8 of 1000 or 375 lb would be required because the weight is moved through a longer distance. To determine the mechanical advantage of the inclined plane, the following formula is used:

F = W sin θ
sin θ = height h / lenght l
where height h = 3 ft, length l = 8 ft , sin θ = 0,375, and weight W = 1000lb
F= 1000 x 0,375
F = 375 lb

Mechanical advantage MA = load / effort = W / F = 1000 / 375 = 2,7

Frictionless Inclined Plane

If there is no friction between the object being moved and the plane, the device is called an ideal inclined plane. This condition might be approached if the object is rolling, like a barrel, or supported on wheels or casters. Due to conservation of energy, for a frictionless inclined plane the work done on the load lifting it, W_out, is equal to the work done by the input force, W_in

Work is defined as the force multiplied by the distance it moves. The work done on the load is just equal to its weight multiplied by the vertical distance it rises, which is the “rise” of the inclined plane

The input work is equal to the force F_i on the object times the diagonal length of the inclined plane.

Substituting these values into the conservation of energy equation above and rearranging

To express the mechanical advantage by the angle θ of the plane,

So

So the mechanical advantage of a frictionless inclined plane is equal to the reciprocal of the sine of the slope angle. The input force F_i from this equation is the force needed to hold the load motionless on the inclined plane, or push it up at a constant velocity. If the input force is greater than this, the load will accelerate up the plane; if the force is less, it will accelerate down the plane.

Resources:

Youtube Video : http://youtu.be/igrMlzHL-qg
Youttube Video: http://youtu.be/yagD_4UMxrg

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