• Force
• Torque
• Gears
• Torque Output
• Simple Gear Train
• Alternate Ratio
• Compound Gear Train
• Gear Ratio and
Velocity Ratio
• Accuracy and
Precision
• Problem
• Objectives
• Procedure
• Testing
• Distance Test
• Angle Test
• Time Test
• Questions
• Proficiency Test #2:
Excel
• Closing

2
2

l
1

l
2
F
2
F
F = Force [lbs. or Newtons] l = Distance from force to point of rotation [ft. or m]

= Torque [ft-lbs or Newton meters]
Equilibrium:

1
=

2

F
1
*l
1
= F
2
* l
2

• Used to increase/decrease torque or speed
• Penalty for increased torque
– small gear turns through larger angle than large gear
– indicated in ratio of revolutions/second
(gear speed) in equation below ( 
1
=

2
) w
1
* R
1
= w
2
* R
2
• Torque and speed inversely proportional
• Velocity ratio equals inverse of gear ratio

• SPUR GEAR: gear wheel having radial teeth parallel to axle

• CROWN GEAR: gear wheel with teeth set in rim perpendicular to its plane crown gear

• WORM GEAR: short rotating screw that meshes with teeth of another gear

• PINION: small cogwheel, teeth of which fit into those of larger gear wheel pinion gear

• Between two other gears to transmit motion from one to other
• Changes direction of rotation
• No effect on ratios
• ODD number
= reverse rotation
• EVEN number
= same rotation idler gear

• Small force (F
1
) used to lift large weight (W
2
)
1
F
R
1
R
2
W
2

1” 2” 4”
Velocity Ratio


Input
Output



1
2
*
2
4
 1
4

n
1 n
2 n
3
Gears with the same size teeth, ratio equal to ratio of number of teeth
(n) on each gear.


Input
Output



Velocity Ratio n
1 n
2
* n
2 n
3
 n
1 n
3

n
6 n
1 n
2 n
5 n
8 n
3 n
4 n
7
Angular velocities of all gears are equal to that of the shaft on which they are mounted
Velocity Ratio


Input
Output


 n
1 n
2
* n
3 n
4
* n
5 n
6
* n
7 n
8

Simple Gear Train
Gear Ratio =


Output
Input


Velocity Ratio =


Input
Output


Compound Gear Train
Gear Ratio =



Driven
Driving 


Velocity Ratio =







Accurate
Precise
Accurate
Imprecise
Inaccurate
Precise
Inaccurate
Imprecise

• Average (mean) 
P
1

P
2

P
3

...

P
N
N
N = # of measurements
P = parameter A p
• Accuracy (error)
= average

P s

A p
P s
= standard
• Precision
(repeatability)


( P n

 high
( P n

) high

)
2
( P n


( P n low

) low )

You have just been hired by an engineering firm that makes robots for sale for a little less than $100.00. Your boss has asked you to build and test this prototype, and to make suggestions for improving the instructions before final printing.

• Suggest improvements to assembly instructions
• Learn importance of understanding instructions and components BEFORE assembly
• Understand related concepts
• Troubleshoot
• Write/Test programs to evaluate performance
• Make necessary calculations

• Take notes as you work to help you answer questions
• Refer to assembly instructions throughout lab
• Analyze components
• Assemble robot
• Understand gear linkages
• Determine gear ratio
• Perform three tests

Draw expected straight line path
• Distance Test
• Angle Test
• Time Test
Results will be used for Excel Proficiency

• Run robot for 3 units of time
• Standard = (Distance traveled by 3) / 3
• Distance robot should run for 5 units of time
= standard value * 5
• Repeat 10 times:
– Run robot for 5 units of time
– Measure the distance
START END

• Use data from the distance test
• Draw straight lines from origin to points
• Measure each angle of deviation ( 
)
• Determine accuracy and precision
• Determine standard
START  END

• Choose distance for robot to travel
(should be more than 2 feet)
• Set robot to run on straight path infinitely
• Measure amount of time robot takes to travel chosen distance (first trail is standard)
• Repeat 10 times using same distance
START END

• Discuss assembly instructions for WAO II.
• Were there any pieces missing?
• What does “M2.3 X 8” mean on a screw?
• Discuss power gear linkages that permit:
– Rotation on axis located in center of robot
– Turning/Rotation on axis outside of center
– Translation/Movement in straight line
• Determine gear ratio/velocity ratio.

• Efficient/Accurate way to count gear teeth
• What crown gear does that spur gear doesn’t
• What are two identical springs for
• Where friction used rather than cement
• Why two plastic pieces were not single mold
• Testing methods and results
• Average values and maximum deviation
• Determine accuracy/precision

• Use results of all three tests
• Follow format in manual
• Include:
– Title page (include source of data)
– Chart comparing your data to someone else’s
– Legends with charts (not illustrated in manual)
– Table of
ONLY your data for each test
(more trials may be included)

• If failed, discuss possible reasons for failure
• Include recorded observations:
– All written observations
– Sheets with plotted data
• Original data must be signed by TA
• Use Excel to organize report data
• Make sure
ALL questions are answered