Creation and study of a first mechanism: the Archimedes’ lever.

[b]Abstract: [/b]This activity involves the creation and study of a first mechanism: the Archimedes’ lever. This mechanism will indirectly allow children to learn concepts related to the weight and volume of objects.[br][b]Keywords:[/b] Archimedes' Lever, Simple mechanism, 3D printer[br][b]Resource list: [/b]one 3D printer, 3d printer filament, common objects like coins, etc.

Archimedes' Lever is one of the earliest and simplest mechanisms in history. Therefore it is easy to understand the concept of cause-effect using a simple mechanism.[br]

The activity described in this document is presented in its most basic form, using an approach that allows, however, a much higher level of complexity. For example, it is possible to include in the activity elements that combine technologies such as Augmented Reality or Virtual Reality, referring specifically to the scope and environment in which the activity will be developed. This activity can therefore be taken as one of the first basic activities to be conducted within the curricular areas of mathematical competence and basic competences in science and technology, including technological systems, machines, and tools.[br][br]The main objective of the activity presented here is showing children the advantages that can be provided by even the simplest machines, such as, in this case the Archimedes lever. By using this lever model, children will be able to understand basic concepts regarding the weight of objects and the effort needed for lifting them, apart from the concept of the lever itself, relating it also to common objects that they can encounter in their daily life.[br][br]Clearly this activity is linked to the Social Challenge related to Education, however, in a more tangential way, it is possible to align this activity with other similar ones that are related to simple green Energy production machines, such as wind turbines, with simple changes in any of the parts described in this document and its assembly.[br][br]1. Archimedes’ lever.[br][br]Archimedes (287-212 BC.C.), was one of the most important scientists of antiquity.  During his many years of research, he made many contributions in very different fields. For example, he is well known for his work in hydrostatics, starting from his famous cry of "Eureka!" from the principle of flotation, or in physics in general, such as the screw that also bears his name. He is also partly remembered in popular culture, for his explanation of the operation of the lever, popularizing the famous phrase: "Give me a foothold and I will move the world."[br][br]The meaning of this phrase is related to the concept of the lever; a very simple Physics concept, which, through a simple mechanism, allows to multiply the force exerted by the user, who obtains a much greater force than the one he applies (as also happens, for example, using pulleys). If we tried to lift any object with our hand, we should apply a force directly on the object. The force to be exerted in this case should be vertical and upwards, always equal to or greater than the weight of the object to be lifted and this means that it has a very clear limitation. To multiply that force, we can precisely use the effect of a lever.[br][br]From a Physics point of view, the lever (Fig. 1) is a simple machine whose function is to transmit a force from its point of application, through the lever, and to the end of it. It is composed of a rigid bar/arm that can freely rotate around a fulcrum. The result of the operation of the lever is to amplify the force to be received by an object that is at the other end of the lever, in response to the application of a force.

The fulcrum must be located between the load (or resistance) and the applied force (or power). Depending on where the fulcrum, the applied force and the load are located, we might be able to use a little force to apply a larger force on the load. Effectively, the longer the arm section between the point where the Bp force will be applied and the fulcrum, as compared to the length of the arm section between the Br load and the fulcrum (Fig. 2), the less force will be needed to achieve the same result on the load. With a sufficiently long (and strong) lever and an appropriate support for the fulcrum, Archimedes could have moved the entire world. Even if this is not possible, the Archimedes lever is therefore a machine that helps us lift heavy loads.[br][br][b]Law of the lever.[/b] In physics, the law relating the forces involved in a lever in equilibrium is expressed by the following equation (Fig. 2):[br]                                                    [math]P\times B_p=R\times B_r[/math][br]Where [math]P[/math] is the force we apply,[math]B_P[/math] is the length between the place where we apply the force [math]P[/math] and the fulcrum, [math]R[/math] is the resultant force applied in the resistance, and [math]B_r[/math] is the length between the place where the resistance is located and the fulcrum.[br][br]Explained in other words, there is a torque (the product of force and distance) associated both to the force we apply, [math]B_p[/math]B, and the force acting over the resistance, [math]B_r[/math]. The law of the lever can also be expressed as the law of moments or torques, which says that the clockwise torque (due to our force) and anticlockwise torque (due to the resistance) must be equal. Therefore, by modifying distances, we get modified forces too.[br]

2. 3D printers[br][br]3D printers have become a very useful tool in order to prepare rapid prototypes, elements in different phases of design and redesign, and also educational environments, being able to create pieces or game elements entirely according to our needs.[br][br]When designing parts to be generated on a 3D printer, we must take into account considerations regarding the size of the parts, since not all printers have the same capacity. In the proposed activity, different designs are presented, one of them involves dividing the parts into smaller pieces, to solve this problem.[br][br]You also have to take into account the handling of the printer, which, although it is not difficult, requires some training and experience, apart from the considerations of the necessary maintenance operations for the 3D printer.[br]

This section describes the activity and the materials that are needed for developing the proposed activity. The parts that make up the machine (lever) have been designed in AutoCAD (Fig. 3), and have been exported to STL files, which is the format used by 3D printers (Fig. 4). However, you can use a free tool such as Tinkercad. Presently, these STL files are available to any teacher who wants to carry out the activity.[br]

Some modifications can be introduced while designing the appropriate STEAM activity, according to the age of the participants. In this sense, it must be taken into account that the set of pieces that make up the system is very simple, and it is not contemplated to make different versions according to the age of the participants, within the framework of early childhood education.  As will be indicated later, it is more appropriate to think about different applications or to play with different elements to be "weighed" on the lever, such as animals, coins or other objects, according to different ages.[b][br][br]Arm-lever (Fig.3-In green):[/b] It is the largest elongated piece that we can see in green, in which we find 3 well differentiated parts. [br][br][list][*]At one end we have the basket, where the objects to be lifted can be placed. It is the resistance point R according to the terminology we have used to enunciate the law of the lever.[/*][*]On the opposite tip of the lever, we have the point where we will apply our force, that is, the point P according to the terminology we have been using so far. It has been designed so that it resembles a hand (cartoon style), for illustrative purposes.[/*][*]Finally, we have the arm itself. It has 7 slots that allow anchoring the arm to the support through a peg-shaped axis, positioning the axis in any of the mentioned 7 slots. According to the chosen slot, we can change the distances between the support and the basket (Br, according to the terminology used), as well as between the support and the hand (Bp, according to the terminology followed so far).[/*][/list]

[b]Balancing support (Fig.3-In blue):[/b] it is the support of the lever, and it is recommended that it is anchored to a surface for the stability of the whole system. It is therefore advised that the material includes, for example, a [b]wooden board[/b], to which it can be glued.  Its function is to permit the rotation of the arm-lever, and depending on the chosen slot, the machine will have different inclination degrees.

[b]Axis (Fig.3-In red)[/b]: This is the axis that serves as a union between the two previous pieces, the arm-lever and the support, and that therefore allows the relative rotation of the arm with respect to the support.

[b]Weights:[/b] For demonstrating the lever operation, it is necessary that we have a series of objects to be placed in the basket. The idea is to be able to play with the different combinations of weights and fulcrum positions. One option, for example, is representing the different weights as animals, being able to play with different types of materials of different density (for example, plastic, wood, metal, etc.) and with different animals, such as a mouse, a horse and an elephant.

[b]Other components[/b] of activity that may be useful could be, for example, a representation of different planets in the solar system. In this case we can represent larger and heavier planets and realize the idea of "raising the Earth".

The educational activities that can be conducted based on this proposal, based on The Lever of Archimedes, are multiple. Below, we present a simple proposal for implementation that can be enriched with other complementary actions, depending on the students’ characteristics, the available resources and the didactic objectives pursued. The content of this section is structured in the following sections:[br][br]a. List of required materials[br]b. Preparation of the Activity[br]c. Activity development [br]                                  i. Pedagogical/didactic objectives[br]                                  ii. Participation/Involvement [br]                                iii. Incorporation into the Activity of the objectives

We close this section with [b]some recommendations[/b] on the basic and complementary materials that can be used in the activity, in situations such as the current COVID-19 pandemic, which requires sanitizing the materials. Since the components of the machine are all 3D printed (Fig. 4), it is easy to clean them after each session, without affecting their wear or subsequent use. It would also be necessary to sanitize the different objects to be used, such as the components used as weights.

In this particular example, the list of materials is the same list given in the section of Activity Components, since only one item in each class will be used. If we want to replicate several levers, evidently, we need to replicate the list of materials given below. Therefore, we will need the following elements for carrying out this activity:[br][list][*]STL files for printing.[br][/*][*]Access to a 3D printer.[br][/*][*]After we print all the components, we will obtain the following ones:[br][list][*]Arm-lever (Fig.3-In green): It is the largest elongated piece that we can see in green[br][/*][*]Balancing support (Fig.3-In blue): it is the system support, and it is advisable to anchor it to a surface[br][/*][*]Axis (Fig.3-In red): This is the axis that serves as a union between the two previous parts[br][/*][/list][br][/*][*]Different weights to place in the basket, such as:[br][list][*] Objects of a similar volume, but of different materials, such as, for example, plastic, wood and metal.[br][/*][*] Objects of the same material, but different volumes, representing for example animals that have different weight, such as a mouse, a horse and an elephant.[br][/*][*]A set of coins that we place in the basket successively, so that the more coins there are, the more force we must apply for lifting them, or we must move the lever’s axis.[br][/*][/list][/*][/list]We will also need to have printed on paper a representation of the lever, such as the one indicated in figure 7, so that it serves to theoretically explain the concept of the lever and that it serves as a reinforcement of the idea of "moving the world".

For this activity it is necessary to create the parts in a 3D printer or to create them in any other way, depending on the materials, parts and tools that we have available.  Some of the pieces are not essential to be 3D printed; for example, the axis can be any object that has a cylindrical shape, such as a pencil. In the case of the balancing support, the same thing can be said: as long as it has a hole similar to the diameter of the axis and the shape and dimensions are fine, other options can be used.[br][br]Once all the elements are arranged, they can be finally assembled, as shown in Figure 5. Additionally, it is necessary to select the elements that we will use as weights, identifying those that weigh more than those that weigh less. It is recommended to have at least 3 different elements or weights that can be easily distinguished.

The arm-lever has 7 different grooves that allow the system to be configured differently (with different relative distances from the support to the places where the force and the load are placed). In consequence, it is possible to obtain different configurations for performing different tests (Fig. 6).

To visualize these different situations (Fig. 6 a and b), the teacher can remove the axis of rotation and position it in another of the different grooves of the main arm. With the same load in the basket, the teacher will teach the children how the effort that has to be applied is larger or smaller, according to the length of the arm (as indicated by Archimedes' law).[br]

i. [b]Pedagogical/didactic objectives[/b]. Describe the pedagogical objectives of the activity. [br][left]The basic activity (and the proposed complementary or enrichment actions, point 3.4) contribute to foster the acquisition of knowledge including observing and exploring the children's environment, developing creativity and initiating children in the knowledge of sciences, among other issues. The Objectives could include:[/left][list=1][*]Understand that a machine/mechanism can help us do tasks that we cannot do alone.[/*][*]Intuitively understand what a lever is. [br][/*][*]Understand that larger animals weigh more (mouse < horse < elephant). Secondarily, they understand that the different materials from which objects are made also contribute to them having different weights.[/*][/list]ii. [b]Participation/Involvement.[/b] Describe the environment of the activity to make it attractive to participants. To achieve this objective, it is proposed that the teacher can perform some or all of the following activities:[br][list=1][*]Introduce the concept of a simple mechanism or machine.[/*][*]Identify an example that children may know, such as a scale that tilts to where it weighs the most, or a seesaw for children to play in the playground.[/*][*]Ask the children what the heaviest thing they can lift.[/*][*]Ask next, if anyone believes that they are capable of lifting, for example, something as big as an adult, the whole Earth, etc.[/*][*]Ask the children if they know what a lever is, without further comment. Let them verbalize different options, explaining their operation, even if they are wrong, before making the formal explanation of the lever.[/*][*]Ask if anybody knows how ancient Greece was, if they have seen it in any series or movie (for example, it is possible that someone has seen the Disney movie Hercules or some similar reference). Prepare an image, such as the one shown in Figure 7. Enunciate the phrase "Give me a foothold and I will lift up the world" and ask if you understand what you mean by it, making a simple explanation.[/*][/list]iii.[b]Incorporation of the objectives into the Activity.[/b] Fit the pedagogical objectives into the environment and story (narrative) that will be used for the activity. That is, to present some guidelines on how to introduce, in a practical way, the objectives to be carried out, in the activity.[br][list=1][*]Once the activity has begun with the questions described in the Participation/Involvement phase, students are presented with 3 possible weights to lift. Each one can be of different material, for example, plastic, wood and metal, but, on the other hand, they could have a similar volume.[/*][*]The weights of different materials are presented to the children, explaining that the animals weigh some more than others, having them check this by themselves.[/*][*]The shaft is placed in an intermediate position of the lever holes, between the axis assembly and the balancing support. The weights are placed in the basket successively and the hand is pressed in each case, checking that it is easier for us to lift them, but that it costs a little more to lift the elephant than the mouse.[/*][*]The position of the shaft and the weights that we put in the basket are varied, so that the children check that the effort changes, and that the lever helps in this task. Additionally, you can play with questions about in which position of the axis it is more difficult to lift the weights, whether the axis is closer to the hand or the basket. Or with questions like “is it more difficult to lift a mouse with the shaft in the position closest to the hand or the elephant with the shaft in the position farthest from the hand? The main idea is to leave it to the children to experiment with all the options and come up to their own conclusions.[br][/*][/list]

The material has been designed in such a way to facilitate student involvement and facilitate the development of different but related activities, based on the use of modified mechanics and game components.  In this section you will find some suggestions for enhancing the proposed basic activity:[br][list=1][*]You can play with the materials. For example, you can talk about coins with materials simulating gold, silver and bronze.[/*][*]You can represent an Earth and put it in the basket so that they associate the image with the famous phrase of Archimedes.[/*][*]It is possible to use the lever for explaining the concept of forces and torques for high school students.[/*][*]You can modify how the lever is used, turning it, for example, into a catapult[/*][*]You can use smaller versions of the system (smaller models for 3D printers are included in the materials provided), or the large system divided into smaller parts that are then assembled (those models are also included).[/*][/list]

Students with learning difficulties and/or low cognitive abilities should get to know the robot individually before performing activities with a group - this will help them better understand the task and be successful in joint activities. When forming groups, keep in mind the different cognitive abilities of different students - sometimes it is useful to create homogeneous groups so that learners with similar opportunities can exchange experiences, but sometimes it is useful to create a heterogeneous group so that one student can help and guide another student. For students with ASD is it very often difficult to make choices and/or solve creative tasks - they should be gently directed to solve a specific task.[br][br][br]

If you do not have access to a 3D printer you can play only with the cited CAD tools, in order to create a virtual set of complements that you could use later when it becomes available or use it only as a 3D design tool. The use of the Thingiverse repository is also recommended to understand that the creation of the models is an optional part of the activity.[br][br][br]

The activity presents an example of a simple mechanism. The idea is to allow that through the creation of simple prototypes, and a series of games, the concept of what a machine is can be introduced.[br]The Archimedes lever is one of the oldest mechanisms in existence. It has been reproduced by design with CAD tools, such as TinkerCAD, a model of the lever, and subsequently 3D printed. The game is complemented by a series of animals of different size and weight, objects, simulation of coins, etc. The mechanism allows you to adjust the length of the lever and thus be able to play with different weights and different lever arms. Other complementary models can be created by means of 3D printing.[br]The participants will have different Archimedes’ levers of different scales, larger or smaller, and on the other hand they will have different lengths of arms. Depending on both the size, the bigger you can lift more capacity, and the length of the lever, the longer it is, you can lift more weight.[br]The game must be played by moving the axis, so that the lever has a longer or shorter arm, teaching children how to increase or decrease its effect of multiplying the force exerted.[br]As discussed above, we do not expect participants to have prior knowledge of machines, mechanisms, or basic physics. But inside the workshop, the participants will get acquainted with the concept of a simple machine, weight and volume.[br][br][b]Workshop[br][/b][br]At the beginning of the workshop, we provide the participants with the vocabulary, terms and concepts necessary to use the Archimedean lever. A small theoretical introduction is also attached where the mechanical concepts to be presented in the activity are explained in a simple way. Then we explain the importance of understanding a first simple mechanism, so that from that knowledge, children can be taught, step by step, increasingly complex concepts.[br]Next, the printing of a simple piece in 3D printing is presented as an example, indicating that this machine potentially allows us to reproduce any object that we want to use in any of our activities. The basic operation of a 3D printer is explained.[br]Once this explanation is done, the TinkerCAD tool is introduced, which allows you to create 3D models in a simple way, without requiring knowledge of technical drawing. A few simple examples are made, so that the participants can create their 3D models ready to print.[br]As a complement, the Thingiverse repository is shown below, where the participants verify that it is not necessary to create new models, since many of them are available in this repository and can be downloaded and used for the activity.[br]We then discussed for a few minutes the ease of use of each of these tools, and the desirability of their basic use, in order to create an unlimited number of components for the games that teachers play with their children in the classroom. Finally, we share our research-based understanding of why 3D designs and printing technologies and other STEAM suites are not yet widely used by teachers. Next, we form three teams, each with a set of levers of different sizes, and continue with the workshop.[br]The teams first have to combine different sets of pieces to be weighed, including commonly available objects such as coins or pencils and erasers, by playing with the different positions of the axis of rotation of the lever and the different sizes of the lever.[br]Finally, each group must find another simple application of the mechanism, as it is, or with minimal changes, being frequent examples that the mechanism becomes a catapult, or, with small changes, a weighing scale.[br]The learning outcomes for the participants are listed below. Each participant is able to:[br][list][*]see the possibilities of using 3D printers and CAD tools as motivating tools in sciences and art classes.[/*][*]use digital interactive learning resources created in GeoGebra.[/*][*]critically evaluate the quality and applicability of the digital learning resource.[/*][/list] [br]The 60 minutes workshop will give teachers hands-on experience and emotion about how they could benefit from using 3D printers, CAD tools, etc. as learning tools during their regular math lessons. We hope to have a fruitful discussion with the workshop participants about the effectiveness of such short workshops. The focus of the discussion is to find out whether these workshops can be used for creating awareness about the benefits of STEAM kits, especially simple mechanisms, and reducing the anxiety towards using STEAM in teaching practices.[br][b][br][br][/b][br]

Archimedes and the Law of the Lever[url=https://physics.weber.edu/carroll/archimedes/theIndex.htm] https://physics.weber.edu/carroll/archimedes/theIndex.htm[/url][br]Ultimaker 3D printers. 3D printing in education[url=https://ultimaker.com/es/applications/education] https://ultimaker.com/es/applications/education[/url][br]Repository of 3D models ready to print[url=https://www.thingiverse.com/] https://www.thingiverse.com/[/url][br]Tinkercad | Create 3D digital designs with online CAD [url=https://www.tinkercad.com/%20] https://www.tinkercad.com/[/url][br]