Key Questions How do gears work? What is the Law of Gearing? How can Gear Ratios be used to design machines?
Overview Build gear machines Deduce the rule for calculating the number of turns for each gear in a pair of gears Apply ratios to design machines with gears Design a gear machine to solve a specific problem
Simple Machines Include: rope and pulley wheel and axle systems gears ramps levers screws
Gears as Simple Machines Simple machines can change the direction and/or magnitude of an Input Force
What are the variables? Teeth – Each sized gear has a particular # of teeth. How many does each size have? Turns – Each gear turns an exact amount of times, which we can count. How many times does each one turn?
Looking at the Results Can you derive a mathematical formula which relates the # of turns of the Input Gear to the # of Turns of the Output Gear? What is the relationship? Use the # of Turns Use the # of Teeth
Mathematical Relationship (Input gear turns x Input gear teeth) = (Output gear turns x Output gear teeth) Make the equation easier to use by substituting Let N i = # of turns of the Input gear Let T i = # of teeth of the Input gear Let N o = # of turns of the Output gear Let T o = # of turns of the Output gear 5.N i x T i = N o x T o
The Law of Gearing N i x T i = N o x T o Can we write it another way?
Complex Gear Machines Make a machine that uses at least 2 pairs of gears- Not this one--- make your own Record the position and # of teeth on each gear in the Data Table Record and count how all the gears rotate Use what you have learned and the table to work out the gear ratios
Looking at the Pairs of Gears Use Table 2 to figure out how to calculate the final gear ratio
Final Gear Ratio Each pair of gears has a gear ratio This ratio (fraction) can be reduced There can be more than two pairs of interfacing gears in total Find the Gear Ratios of all pairs
Final Gear Ratio Reduce each Gear Ratio fraction from Table 2 12:24 = 12/24 = 1/2 Multiply all Gear Ratio fractions ½ x ½ = ¼ = 1:4 This is the Final Gear Ratio
1:4 or 4:1? The gear ratio depends on what gear you use as input and what gear you use as output. If the final gear ratio fraction is less than 1, like 1:2 = ½, the output gear turns less than the input gear. This is used for power, like when using a low gear to go uphill on a bike. If the final gear ratio fraction is more than one, like 4:1 = 4/1, the output gear will turn more than the input gear. This is used for speed, like using a high gear when going really fast downhill on a bike.
Designing Gear Machines What is the objective? Speed vs. Power What is the desired Final Gear Ratio? – factor it to lowest possible values Look at the gears you have to work with Use the available ratios to get the final gear ratio you need How about spin direction?
Factoring Gear Ratios Example Gear Ratio Desired – 6:1 Factor 6/1 3 x 2 = 6 Check Available Ratios – 1:3, 1:2, 2:3, 3:1, 2:1, 3:2 Is it possible? Yes 3/1x 2/1= 6/1= 6:1 Attach Gear pairs that give desired Final Ratio It may require more than two pairs of gears
How Can You Make- 9:1 4:1 18:1 The highest possible ratio with the gears provided 3/1 x 3/1 = 9/1 2/1 x 2/1 = 4/1 3/1 x 3/1 x 2/1 = 18/1