Teacher Mechanics
Gears Gear Ratios / Pulleys
Note to the teacher
On this page, students will learn how to apply the concept of gear ratio to pulley combinations. Gear ratio is defined as the
number of times the driving axle must revolve in order to make the driven axle revolve exactly once. In this page, students
will learn to determine the gear ratio for pulleys by dividing the diameter of the driven gear by the diameter of the driving
gear. They will then convert the measurement units from centimeters to inches, and divide the diameters to determine the
gear ratio. Students will have to use decimals to make these calculations. While the worksheet is designed to help students
learn how to determine gear ratio and to convert measurement units, and may be successfully completed by students with
little background in these areas, the existing ability to multiply decimals will be necessary to successfully complete the
worksheet. Teachers may wish to review any or all of these skills depending on their students’ background. Note that there
are no instructions regarding rounding. The answers assume rounding to 2 digits beyond the decimal place, except for
known fractions. Teachers may wish to supply additional instructions. If they do not, students’ answers may vary slightly
according to what rounding conventions they use.
Instructions
Given the pictures of pulleys on your left please answer the following questions. What is the gear ratio for the
combination? How many times must the driving pulley go around for the driven pulley to make one revolution?
Note: The driving pulley is always on the right. Possible pulley diameters are 3.5, 2.3 and .6 centimeters.
Use the conversion formula below to convert units from centimeters to inches.
Centimeter
1
Inches
=
.39
1.
(Diameter of driven pulley in cm)
3.5
=
.6
(Diameter of driving pulley in cm)
Gear Ratio
(Diameter in inches)
1.37
.23
=
5.96
or
5.83
*
(Diameter in inches)
* Due to round-off errors.
5.47
©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Gears Gear Ratios / Pulleys
Students are expected to use the following procedure:
•
•
•
•
•
Identify which of 3 pulleys is pictured, and find the correct diameter from the instructions and example.
Enter the correct values in the boxes labeled “(Diameter of driven pulley in cm)” and “(Diameter of driving pulley in cm)”
Use the conversion formula to convert these values to inches
Enter the converted values in the boxes labeled “(Diameter in inches)”
Divide the values in inches to determine the gear ratio
Approximate classroom time: 10-15 minutes depending on students’ background
Students successfully completing the worksheet will be able to:
1.
2.
3.
4.
Define gear ratio
Identify gear size by measuring the diameters of pulley combinations
Convert centimeters to inches
Determine gear ratio from pulley combinations of different sizes
Standards addressed:
Math Standards
Numbers and Operations
Algebra
Geometry
Measurement
Problem Solving
Connections
Technology Standards
The Nature of Technology Standard 1
Design Standards 8, 9
Abilities for a Technological World Standard 12
Using Technology to Design the Future Standards 16, 18, 19
Science Standards
Content Standard B
Content Standard E
Note: Workbook answers begin on the next page.
©2005 Robomatter Inc. RE 2.5_RW 1.1
5.48
Teacher Mechanics
Gears Gear Ratios / Pulleys
Instructions
Given the pictures of pulleys on your left please answer the following questions. What is the gear ratio for the
combination? How many times must the driving pulley go around for the driven pulley to make one revolution?
Note: The driving gear is always on the right. Possible pulley diameters are 3.5, 2.3 and .6 centimeters.
Use the conversion formula below to convert units from centimeters to inches.
Centimeter
1
Inches
=
.39
For all answers, the gear ratio of a pulley is always the diameter of the driven pulley divided
by the diameter of the driving pulley:
1.
(Diameter of driven pulley in cm)
3.5
=
.6
2.
(Diameter of driven pulley in cm)
(Diameter in inches)
=
1.37
.90
(Diameter of driving pulley in cm)
(Diameter in inches)
(Diameter of driven pulley in cm)
(Diameter in inches)
2.3
=
.6
4.
.23
(Diameter in inches)
2.3
3.
1.37
(Diameter of driving pulley in cm)
3.5
.90
.23
(Diameter of driving pulley in cm)
(Diameter in inches)
(Diameter of driven pulley in cm)
(Diameter in inches)
2.3
=
3.5
(Diameter of driving pulley in cm)
NAME
Gear Ratio
(Diameter in inches)
.90
1.37
5.96
or
5.83
*
=
Gear Ratio
1.52
=
Gear Ratio
3.91
or
3.83
*
=
Gear Ratio
=
.66
(Diameter in inches)
* Due to round-off errors.
DATE
5.49
©2005 Robomatter Inc. RE 2.5_RW 1.1