## Introduction: Rotation Machine

The device designed for the showing of a suspended object is similar to the specimens of a gyroscope or particle contained in the Museum of Science and Technology, except that it has a different use and a measuring instrument is installed on it. These concentric circles are perpendicular to the three coordinate axes and can be rotated around the axes at an arbitrary degree. The rotation or rotation matrix of an object in space is obtained by having these three angles, which are useful for dynamic calculations and determining the orientation of an object in space. In addition, students can visualize concepts of aerospace rotation such as rolling, torque and rotation angles, and at the university level how to perform and analyze dynamically in three-dimensional space for a popular example, such as a gyroscope. Showed. In addition, at higher levels of science, concepts such as the Quaternary or Quaternary can be displayed to those interested in the field. One of the great benefits of this design is the simple and low cost design of this machine with the help of 3D printers and a few magnets, in various sizes and sizes. Portability, the ability to expand and freedom of action can also be added to these benefits. In addition, you can upgrade the device by adding new designs and adding users.

## Step 1: How It Works

The device is very simple to make and the way it works is that the user can read the rotating angles in the three main three-dimensional space for the center object of the device and use those angles for scientific work. Like getting the rotation matrix and ...

Aiming of this Design:

A) Understanding the concepts of the rotation and orientation of any object in space and familiarity with its practical examples.

B) Measurement of the rotation matrix of any desired object (a plane model) by Euler method or by other methods available in dynamics and aerospace. You need to have a manual or a table containing calculations to help with the device.

(C) converting a science project that is a bit complex into a product that is simple to construct and that the puzzle can be described as a commercial educational or intellectual entertainment product. This action reinforces the creativity in the realization of scientific ideas in adolescents and introduces the benefits and benefits of 3D printers and the practical use of magnets.

D) Close experience of visitors and students with a teaching model: Consider a cheap, plastic sample made that users can capture and work with, and a limitation on how much they can be damaged or depreciated. It does not have the artistic or price tag found in museums and laboratories

Applied Aspects: To understand the meaning of these rotations and familiarize themselves with a simple example such as the gyroscope of mechanical and aerospace engineering students in the Advanced Dynamics and Dynamics course, they can solve an example by hand.

Another concept that can be shown to students is the inclination of a plane or space object with their three angles pitch, roll, yaw, or their Persian equivalent to the angles of rotation, torque and rotation. Its appealing to audiences: In addition to what was said to be appealing to audiences, multipurpose use or finding other uses for audiences can be mentioned; adding different shapes and designs to the device Or, on the other hand, turned the device into astronomical and astronomical instruments or .... It is enough to provide banners or manuals such as what was said for the rotating angles. For example, one can model the direction of the sun's or a planet's motion by pointing the device at the sky.

## Step 2: Scientific Base

Each rotation in three-dimensional space can be represented by 3 angles that are rotated around the three reference coordinate axes. On the device, rotate the object with degrees embedded on the three axes of the coordinate, then record 3 angles around z, y, x such that the right-hand rotation is about sixty, counterclockwise (positive). do. These 3 angles in different ways such as rotational matrix, Euler or Quaternion angles can give the rotation or inclination of the object in 3D space to be used in dynamic computation. This device is more designed to represent the concept because it does not have the degree of precision required for millimeter calculations, and the computer must be used for precision or quaternary calculations. But you can do the same with less precision with these three angles on paper.

Rotating Matrix Calculation:

Assign the above three angles to the following matrices: Consider the angle θ for each matrix around the same axis written in degrees or radians depending on the type of angle displayed on the device.

https://en.wikipedia.org/wiki/Rotation_matrix

https://en.wikipedia.org/wiki/Euler_angles

The Quaternion theme is widely used for spacecraft, satellites, or rockets in the air, but its concept is difficult to grasp with the notion that any era in 3D space can be With a positive vector and the angle of its rotation, the vector showed space, that is, a 4-parameter vector that has one scalar and three vector parameters. As can be seen in the figure below, this concept can be illustrated by the free vector in the device. But you can't measure quaternion directly with this machine and you have to use a computer to measure it. Another way is to use a tool in MATLAB software that gives these three angles the output of the quaternion machine. It calculates and the test is not without grace. The use of quaternion instead of bulk rotary matrices has many advantages and applications, see the following link :https://en.wikipedia.org/wiki/Quaternions_and_spat...

## Step 3: Lets Making One

First we design a few rings that can rotate inside each other, these rings are hinged by the magnet. And at the end of each loop is a circular graduated plate showing the angle of rotation of that loop relative to the previous loop.The middle shape can be designed to be interchangeable.

You can use plain bearings or hinges to hold the rings together instead of the magnet. You can also make it with other materials or recyclables instead of 3D printing.

Modular, simple and lightweight, you can digitize it with the help of an Arduino and a few small servo motors and capture the amount of rotation of the object in 3D with direct programming on the Arduino and maybe better ways.

## Step 4: Files

Files needed to build this device:

3D parts file for 3D printing and scaled plate for pasting at installation with degree marker to be attached to inner ring. Inside the rings is a place for small thick circular magnets that you can easily handle.

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