Discover: Discover: Learning about: & Worm Drives Learning about: Gears & Worm Drives What is a and how is it used? What is a gear box? Relation between force and speed How does the gear’s diameter affects speed Gear ratio What is gear ratio and how is it calculated? Have you ever thought how the huge and heavy cargos are and power? The gearbox concerns any combination or assembly of gears and loaded or removed from ships? Dockside cranes are responsible can be found in a variety of devices: from the smallest wrist for this process and are essential for every commerce port. In watch to the biggest train! In this experiment we will learn all this experiment you can build a similar type of dockside crane about this ingenious assembly, which allows us to control the Level Of Difficulty Level Of Difficulty model and learn more about gears and how they are used. speed of any machine.

1. Complete the following table according to your 1. Complete the following table according to your Materials Needed: Materials Needed: measurements and observations. Mark with ü the appropriate measurements and observations. After you take all - Engino® Simple Machines (STEM40) or Gears - Engino® Simple Machines (STEM40) or Gears boxes for FORCE and LIFTING SPEED. Results may vary but trend should measurements, complete the FORCE row with the word: easy, & Worm Drives (STEM05) or Master Set & Worm Drives (STEM05) or Master Set stay the same. medium, difficult and most difficult. Also, fill in the last row (STEM50). 1. 2. 3. 4. (STEM50). with a simplified ratio of input revolutions to output revolutions.

CASES 1. 2. 3. 4. Procedure: Procedure: 1. Find the instructions in page 28 and build 1. The base of the gearbox will be step 4 of the experimental crane model. For case 1 the experimental crane in page 28. For case Crank’s revolutions 105 12 7 155 make the first gear assembly of page 29. 1 make the first assembly of page 31. easy CASES output output input input input 2. Position the experimental crane on a table FORCE medium 2. In the experiment we need to measure output output input (difficulty) and lower the load (weight) down to floor difficult how many revolutions the output shaft

level. Then wrap and tie the string around the the most makes when the input crank rotates. Two axle, so it becomes tight. This should be the difficult people are needed for this: one should turn slow starting point for every case. the crank slowly with the appropriate INPUT 1 10 15 30 medium number of revolutions (as stated in the table) LIFTING 3. Turn the crank and measure how many SPEED and the other should measure the output fast OUTPUT 15 15 10 2 revolutions are needed until the load reaches revolutions. You can connect another crank the top (orange pulley). Write your answer in the fastest at the shaft of the output gear to help you the next table for case 1. Also, try to feel the measure the revolutions with more ease. FORCE most difficult difficult medium easy amount of force you have to apply in order to 2. Look at the “FORCE” row and the “LIFTING SPEED” row of the lift the load and observe the lifting speed. table and write your conclusions regarding the relationship 3. For case 1, revolve the input crank 1 time INPUT 1:15 2:3 3:2 15:1 OUTPUT between the force applied and the elevation speed of the load. (1 full circle). While measuring revolutions, 4. Repeat the same procedure for cases 2, 3 feel the amount of force you apply. 2. Why the gear ratio (input revolutions to output revolutions) is and 4, in which the gears are assembled as in The different gear assemblies require different amount of force in different in each case? What about ? pages 29 and 30. Try to keep the same order to lift the weight. The more force is needed (more difficult in 4. Repeat the same for the remaining cases. turning pace in each case. Write your findings For case 2, make the second gear assembly In cases 1 and 2, the output speed is increased and the Torque is in the table about the crank’s revolutions. terms of effort), the fastest is the lifting speed of the load and vice of page 31 and turn the crank 10 times. For decreased, as one gear drives a smaller one. In cases 3 and 4, speed versa. case 3 make the third assembly in page 32 5. Compare the amount of force you used in and turn the input crank 15 times. Finally, for is decreased and Torque is increased as one gear drives a larger one. each case ticking the words easy, medium, case 4 make the fourth assembly in page 32 difficult, the most difficult. Also, compare and turn the input crank 30 times. 3. Make the following calculations concerning the gear the lifting speed with the words slow, 3. Complete the conclusion below using the words in the box. assembly of case 1 and compare your result with the medium, fast and the fastest. Each word 5. Write down how difficult it is to turn the decrease, smaller, driver gear, driven gear, force, increase input/output ratio you found in the table above. What is the should be ticked once. crank for each case at the FORCE row, using connection between the number of teeth ratio and speed ratio? the words: easy, medium, difficult, and To increase speed, the ...... driver ...... gear has to 6. Complete the conclusions in exercises 2 most difficult. In the last row divide the 6 teeth of small gear gear gear and 3. driven gear INPUT by the OUTPUT revolutions and write it gear pair 1 = = x be bigger than the ...... , while to pair 1 pair 2 as a simple ratio. Then, answer question 2. teeth of medium gear 18 ...... decrease speed the driver gear has to be 6 6 6 1 teeth of small gear = x = bigger 6. Measure the number of teeth of each gear: gear pair 2 = = ...... than the driven gear. However, what 18 30 15 large, medium and small. Then, look carefully teeth of large gear 30 force at the gear assembly of case 1. There are two The ratio of the number of teeth (output gear teeth/input gear teeth) ® you gain in speed you lose in ...... and vice versa. Engino experimental crane model pairs: 1) a medium gear connected with a is the same as the speed ratio (input speed/output speed). small one and 2) a big gear connected with a 19 small gear. Keep this in mind for exercise 3. 20 Discover: Discover: Learning about: Gears & Worm Drives Learning about: Gears & Worm Drives How can you change the plane and How can we transfer motion in a gear Carousel direction of rotation? Transfer of motion system? Many amusement parks have at least one carousel, either with Did you know that helicopters have two rotors? They have one wooden horses or swings. The carousel rotates with the help of big rotor which makes the helicopter fly and a small tail rotor, gears, while cam mechanisms move the horses up and down, which rotates in a different direction! The tail rotor is required to creating the illusion of galloping. Its seats hang from the rotating balance the helicopter otherwise it would just spin in the air! Now Level Of Difficulty Level Of Difficulty table, which rotates faster and faster, elevating people to the top. you can experiment with your own Engino helicopter.

1. On the following picture, identify the input and output of the 1. Which part of the helicopter rotates faster: the tail crank or Materials Needed: Materials Needed: model and write it down in the appropriate box. Show also with the main rotor? - Engino® Simple Machines (STEM40) or Gears - Engino® Simple Machines (STEM40) or Gears arrows the direction of each motion. The main rotor rotates faster than the tail crank. & Worm Drives (STEM05) or Master Set & Worm Drives (STEM05) or Master Set (STEM50). (STEM50). output 2. What happens if we rotate the main rotor manually? Procedure: Procedure: 1. Find the instructions in pages 33-35 and 1. Find the instructions in pages 36-38 and When the main rotor is rotated manually, the crank rotates as well input build the carousel model. build the helicopter model. Note that the meaning that the gear assembly works in both directions. teeth of the two gears should mesh tightly 2. Play a bit with your model in order to together in order to take accurate 3. Count the number of complete revolutions of the main rotor understand how it works. Turn the crank measurements. when the tail crank rotates 5 times and write it in the box (handle) slowly at first, then faster and below. observe what happens. 2. Turn the crank located on the tail of the helicopter and observe what happens. Then Revolutions of the main motor 15 3. Identify the input and output motion of rotate the main motor (the big blades) of the when the crank is turned 5 times your model and complete exercise 1. CRANK’S CAROUSEL’S helicopter with your hand and answer REVOLUTIONS REVOLUTIONS questions 1 and 2. 4. Compare your results with your answers in the previous 4. Now, compare the revolutions of the input 1 1 experiment of the carousel model. Are your results the same crank with those of the carousel (seats) and 3. Now turn the crank slowly for 5 times and this time? Why? complete the next table in exercise 2. For 2. Complete the next table 2 2 count the number of complete revolutions of The results are different, because the medium gear in the helicopter easier and more accurate measurements of according to your the main rotor. Write your result in exercise 3 3 the carousel’s revolutions, it is better to turn measurements in step 4. 3 and compare it with the previous increases the speed, while in the carousel the medium gear is idler. the crank slowly. Then explain your results in experiment of the carousel in exercise 2. exercise 3 and answer exercise 4. 3. Discuss the results of the table above in reference to the gear 5. Calculate the gear ratio (also called velocity ratio) of your assembly used for rotating the carousel. 4. Count the number of teeth of the helicopter model in the space provided. 5. Finally, in exercise 5, there are 2 pictures The results are the same, so the input and the output speeds are connected gears and calculate the gear ratio of hand-drills: the Engino model and a real in exercise 5. teeth of medium gear 18 equal. The medium gear decreases speed at first as it is driven by a gear ratio = = _ gear ratio = 3 one. Observe the gear assembly on the teeth of small gear 6 pictures or even try to build the Engino smaller gear, but then it becomes the driver for another small gear. 5. Finally use your knowledge gained so far

model and then answer the question. and complete exercise 6 with the gear 6. Below you can see a diagram (gears A, B and C) in assembly diagram. 4. How is the medium gear called in this specific gear assembly? which gear A is the driver and turns in a counterclockwise The medium gear is called idler gear as it is not connected directly direction as shown by the arrow. Observe it carefully and answer the following questions: to any of the axles and it is only used to transmit power between the A input and output gears. a. Which direction does C gear B follow? Show by 5. How many gears exist on each model below? Circle the gears on the arrow as well. Engino hand-drill and connect them with the respective gears on the b. Which direction does real hand-drill. gear C follow? Show by arrow as well. B

c. Does gear C revolve faster or slower than gear A? Explain why. Engino® hand Gear C revolves faster than gear A because the driver gear (A) is Engino® carousel model drill model Real hand-drill Engino® helicopter model larger than the driven gear (C), while gear B is idler gear. 21 22 Discover: Discover: Learning about: Gears & Worm Drives Learning about: Gears & Worm Drives How to calculate the mechanical What is a worm drive and what is its Mechanical advantage of screws advantage of a ? Worm drive Mechanical Advantage? The extraction of olive oil is a procedure occurring since antiquity. In real life, we can find all sorts of different types of cranes. One What is a rachet mechanism? Our ancestors ingeniously designed olive presses, that were of them is the rotating crane, which can be used to lift heavy manually operated and consisted of a huge wooden screw that loads while locked in place, to transfer them from left to right or moved a big plate, which then pressed the olives inside a barrel. opposite. Follow the steps of the next experiment and build your Level Of Difficulty Level Of Difficulty The same principle is applied even today in modern presses. own fully functional model of a crane with rotating arm!

1. Can you complete the boxes below with the input and 1. Write the number of crank revolutions that are needed for a Materials Needed: Materials Needed: output forces of the screw press model? Also, in the space full rotation of the crane, as well as the number of teeth of the - Engino® Simple Machines (STEM40) or Gears - Engino® Simple Machines (STEM40) or Gears provided, write the types of motions involved. big gear. Compare the two numbers and explain your findings & Worm Drives (STEM05) or Master Set & Worm Drives (STEM05) or Master Set in reference to the worm drive mechanism and the big gear. The handle of the press is (STEM50). input (STEM50). crank revolutions = ...... 30 number of teeth of big gear = ...... 30 - A ruler. moving in a rotating motion - A small bag with sand or beans. The numbers are the same. This means that one full revolution of which converts into the crank corresponds to one tooth movement of the gear. Procedure: output reciprocating motion of the Procedure: 1. Find the instructions in pages 39-40 and 1. Find the instructions in pages 41-44 and 2. Try to rotate the arm directly by pushing it with your hand. build the screw press model. plate. build the crane with rotating arm model. Does it move? Explain briefly why this happens, referencing the types of motions involved. 2. Play a bit with your model and identify the 2. In order to take some measurements, we 2. Complete the gaps below according to your measurements in The arm of the crane does not move when pushed by hand, meaning type of motions that occur as well as the case 1 (step 4 of the experiment). Then calculate the need to create an extended crank. Place the input and output forces. Complete exercise 1 mechanical advantage (M.A.) of the screw press model by following assembly on the large axle of the that the mechanism works only if a rotational motion is applied on making use of the formula below. model. the crank, transferred to the worm drive and the big gear. 3. Turn the handle until the screw is small place this end large completely removed from the press. Then on the big axle medium gear take your ruler and a piece of string from of the model 3. What do you observe when the your Engino package, in order to make rachet mechanism is released? measurements and calculate the mechanical 3. Calculate how many crank revolutions are Give some examples where this 1 2 3 4 5 6 7 8 9 10 advantage of the screw press model, in two needed in order for the arm of the crane to mechanism is used and why. 162.5 32.5 cases. screw’s threaded length = ...... mm screw’s length = ...... mm complete a full circle. Then count the number rachet mechanism of teeth of the big gear and complete We observe that the load drops down. The rachet mechanism is used 4. For case 1, take the string and pass it screw’s threaded length 162.5 exercise 1. Note that the Engino screw tightly around each thread from one end of M.A.= = ⇒ M.A.= 5 in cranes for safety reasons, as they secure the load and in socket screw’s length 32.5 behaves as a worm drive in this case the screw to the other. Hold the two ends, because it is driving another gear. wrenches giving free turning on one side and screwing on the other. stretch the string on a ruler and measure 3. Complete the formula and the gaps below according to your screw’s threaded length in mm (see picture 4. Try to rotate the arm directly by pushing it measurements in case 2 (step 5 of the experiment). Then 4. Observe the following examples and write below if they in exercise 2). Then measure the whole with your hand and complete exercise 2. calculate the mechanical advantage (M.A.) of the screw press represent a worm drive or screw mechanism. screw’s length again in mm (as in next model by making use of the last formula. picture) and complete exercise 2. 5. Note the orange part that touches the medium gear on the top of the model. It is screw’s threaded length 162.5 32.5 6.5 5. Case 2 is a bit more tricky. First, we need to circumference = = =...... pitch = ...... mm called rachet mechanism. Place a load (e.g. number of crests 5 find out the circumference of the screw, bag of sand) on the string. Turn the medium which is the ratio of screw’s threaded length gear in order to lift the load and release the circumference 32.5 (found in case 1) to the number of crests. M.A.= = ⇒ M.A.= 5 mechanism while the load is hanging in the pitch 6.5 Opening a bottle A head Spiral staircase Crest is one complete round of the teeth. air. Write your observations in exercise 3 and screw worm drive screw Then we need to measure the pitch in mm, complete exercise 4. 4. Both answers should be the same if your measurements which is the distance between the crests of were taken carefully, because in exercise 2 the M.A of the screw adjacent teeth. The ratio of the pitch to the press is calculated in full scale, whereas in exercise 3 is circumference is the mechanical advantage calculated by isolating a single thread. Write in the space of the screw. Complete exercise 3 (using the provided what the above mechanical advantage practically given formulas) and the conclusion in means in reference to the distances travelled and force applied. exercise 4. A motor A lightbulb Grape crusher The handle must cover a distance of 325 mm in order for the plate Engino® crane model worm drive screw screw to move 65 mm, but 5 times less force is required (M.A.). with rotating arm 23 24 Exercise 4 Quiz Below, there are three columns: the first with pictures of gears, the second with their names and the last one with their characteristics. Can you join the gear type with its name and its characteristics? (3 points)

A gear train including one Exercise 1 or more compound gears Complete the paragraph below using words from the box (2 points) which significantly changes the speed of rotation output speed, mesh, driver, between, (increase or decrease). driven, direction, reversed, maintain, bigger, idler gear idler gear Converts rotational motion to linear. mesh direction reversed When two gears ...... directly, the ...... of rotation is ...... idler gear If we want to ...... maintain the same direction of rotation, an ...... Works only in one direction between worm gear is needed, positioned ...... the other gears. while reducing the speed output speed driver bigger In order to increase the ...... the ...... gear should be ...... than significantly. driven the ...... gear. Connects two gears Exercise 2 gearbox () that are not near while keeping the Complete the diagram using words from the box (1 point) same direction of rotation.

pitch point circular thickness rack and Changes the direction of rotation by 90 degrees. root, pitch circle, pitch, pitch point, pitch circle tooth, circular thickness, pitch circle

Maintains the same pitch circle direction of rotation tooth between the driver and driven gear. root pitch Exercise 5 The following gear system consists of 4 gears. Gear A is the driver gear and has 80 teeth, gears B and D have 20 Exercise 3 teeth and C has 40 teeth In the right picture, you can see a standard gear A train which transfers motion from the large gear to a) Can you calculate the velocity ratio (V.R.) of this gear system? (2 points) the other large gear through the medium one (idler C gear). Can you suggest a way to transfer the same V.R. = V.R.1 x V.R.2 _ D teeth of gear B teeth of gear D motion without using an idler gear, while still V.R. = x _ keeping the same direction of rotation? Explain teeth of gear A teeth of gear C 20 20 1 1 your idea and draw it in the box provided (2 points) V.R. = x = x _ 80 40 4 2 B V.R. = 1:8 The idler gear can be replaced with a chain drive that will connect the two large gears. This will maintain the same direction of rotation for b) If the diameter B is 200 mm, can you find the diameters (D) of gears A, C and D? (2 points) both gears, the same gear ratio and can even connect them within a DB NB longer distance. V.R.1 = = _ DA = DB x NA = 200 x 80 _ DA = 800 mm DB = DD _ DD = 200 mm

DA NA NB 20

DD ND V.R.2 = = _ DC = DD x NC = 200 x 40 _ DC = 400 mm

DC NC ND 20 25 26 Exercise 6 Complete the diagram of a screw using words from the box (2 points)

shank crest pitch thread, crest, head, length, pitch, nut, shank

head nut

thread

length

Exercise 7 Write down at least four tools that we use for tightening screws (2 points)

The major tools used to tighten screws are: 1) screwdrivers, with either slot head or cross head, 2) allen keys, with hexagonal head for screws with hexagonal hole, 3) spanners, for nuts and screws with hexagonal head and 4) adjustable wrenches, with adjustable mouth for different screw sizes.

Exercise 8 A circular saw, similar to the one in the next picture, works by means of a worm drive, where the worm rotates a wheel which is attached to the blade in order for the device to cut something. Can you calculate the gear ratio of the worm drive, if the worm wheel has 40 teeth? (2 points) number of worm gear’s teeth 40 gear ratio = = = 40 number of worm drive’s teeth 1 This means that the wheel rotates 40 times less than the motor of the saw, but with 40 times more force.

Exercise 9 Connect each type of screw with its name (2 points)

Slotted Cross-shapped Robertson’s External hexagon Square Internal hexagon head screw head screw head screw head screw head screw head screw

Visit our online resources to find the solutions of all the activities: www.engino.com/solutions/stem05

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