With the continuous improvement in the demand of mechanical products, classical mechanisms are moving forward to modern complex mechanisms, which changed from fixed topology to variable topology and from weak coupling to strong coupling.
Variable topology and strong coupling of the cube body gradually attracted attention. The use of the rotation of the cube mechanism can achieve the desired position or form of movement, so that different ends of the actuator can complete a task in order in a certain position, or make different ends of the actuator work together to complete a job with orderly cooperation.
If this design can be applied to a machine tool holder or the manipulator of a mechanical arm, the flexibility of clamping and operation will be greatly improved. If this characteristic can be applied to other mechanical products, it will promote the miniaturization process of mechanical products.
According to the above application ideas, the application of the cube structure also requires basic theoretical research.
The movement of the product to achieve a certain direction involves the research of degrees of freedom in order to achieve the required form of movement and specific state related to the structural mathematical expression and the metamorphic properties. Subsequent research on specific static, friction, control, and other topics will be involved. This can lay a theoretical foundation for applications of the cube mechanism and promote special cube mechanisms from educational toys to machinery such as robots, aerospace, etc.
Some achievements in theoretical research and application have been made. It is of great significance to study the cube mechanism and to promote the development of the cube structure. The topology theory of the cube mechanism has yet to be further studied. The cube. T de Castella. BBC News Magazine. BBC, []. Daily Mail Reporter. V D Stephen. Google Scholar. T Jerome. London: The Independent, Carlisle, P Rodney. J Ori.
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In a cube that is 5x5, 61 cubes can be seen. In a cube that is 6x6, 91 cubes can be seen. The question is: Explain how you could find the number of small cubes that are visible and hidden in a cube of any size. A cube is three-dimensional so the cubes you mention are 3x3x3, 4x4x4, 55x5 and 6x6x6.
Now I can see where the numbers come from. The goal of a Rubik's Cube puzzle is to start with some randomized and shuffled messy configuration of the cube and, by rotating the faces, get back to the original solved pattern with each side being a single color. Actually solving the puzzle is notoriously tricky.
It took Erno Rubik himself about a month after inventing the cube to be able to solve it. Since then, several methods and techniques have been developed for solving a Rubik's Cube, like this basic strategy laid out on the official Rubik's Cube site.
Practiced cube-solvers can complete the puzzle in a matter of seconds, with the current world-record holder solving a cube in 3. Puzzles like the Rubik's Cube are the kind of thing that fascinate mathematicians. The toy's geometrical nature lends itself nicely to mathematical analysis. Any solution to a particular Rubik's Cube configuration, then, can be thought of as the list of basic moves needed to return that configuration to the starting solved state.
One immediate and obvious question, dating back to the original invention of the cube, is, given a particular configuration of a cube, what's the smallest number of moves needed to solve the puzzle?
Relatedly, what is the smallest number of moves needed to solve any configuration of the Rubik's Cube, a number that cube aficionados refer to as "God's number? As Erno Rubik put it in a recent interview with Business Insider , this question is "connected with the mathematical problems of the cube.
Amazingly, it took 36 years after the invention of the toy to come up with an answer. In , a group of mathematicians and computer programmers proved that any Rubik's Cube can be solved in, at most, 20 moves. One reason it took so long to answer such an apparently straightforward question is the surprising complexity of the Rubik's Cube. An analysis of all the possible permutations of where the smaller constituent cubes often called "cubies" can end up shows that there are about 43 quintillion — 43,,,,,, — possible configurations of the Rubik's Cube.
Going through and trying to find the shortest solution for every single one of those configurations, then, is essentially impossible. The key to answering a question like finding the smallest number of moves to solve any configuration is to take advantage of the relationships between different configurations.
In , mathematician Michael Reid found a Rubik's Cube configuration called a "superflip" and proved that it required at least 20 moves to solve. That sets a lower limit on what God's Number could be.
The remaining question, then, is whether or not there are any cubes that need more than 20 steps to solve.
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