Transcript First Class Lever

To do in class
• Mechanical design is an important component
of this class – how it relates to your project
• What you want to learn?
• What you plan to do?
Kinematics
• The study of motion without regard to the
forces or mass of the things moving.
• Kinematic diagrams are scaled drawings
symbolizing how mechanisms work.
• We studied robot kinematics in Fall but we did
not take into account forces.
Examples of
machines
1. Gears
2. Pulleys
3. Chains
4. Cams
5. Bearings
6. Wheel and Axle
7. Inclined Plane
8. Wedge
9. Screw
10. Lever
11. Cranks and sliders
12. Ratcheting mechanisms
13. Clutches
14. Brakes
Machines and Tools
1. Machines and tools are mechanical devices
that work by transmitting or converting
energy.
2. Machines are made up of a variety of
mechanisms.
3. What are some examples of machines?
Simple Machines
Screw
Inclined Plane
Wedge
Pulley
Wheel and Axle
Lever
All of these are related to robotics.
Think how?
Mechanisms
1. Mechanisms help extend human capability by
creating some desired output or motion.
2. A mechanism takes an input motion or force
and creates a desired output motion or force.
Motion
or force
MECHANISM
Motion
or force
Types of Motion
• Common types of motion:
– Linear
– Reciprocal
– Rotary
– Oscillating
All these have
applications in robotics
Definitions:
Energy: Ability to do work
Work= Force x Distance
Force: A Push or a Pull
Linkages
Rotating Arms
gear
Torques are large
bolted to arm
motor
Use counterweights and gears to
compensate
Attach the gear to the arm
Attach the motor to the robot
driven gear
Role of Linkages
• Linkages transmit the motion or force to the
desired output location.
• Linkages:
1. change the direction of the force
2. Change the length of motion of the force
3. Split the motion and force over multiple paths
– Downward motion at one end
results in upward motion at the
other end.
– Depending on where the pivot
point is located, a lever can
multiply either the force applied
or the distance over which the
force is applied
Lever
Pivot point, fulcrum
http://www.csmate.colostate.edu/cltw/cohortpages/viney/balance.html
Explanation
Simple Lever Machine
• This simple machine is based on the position of the
effort force, resistance force, and fulcrum.
• First class lever
– Fulcrum located between effort force and
resistance force
– Usually used to multiply a force
– Example: Seesaw
Resistance
force
This kind changes the
direction of force.
R
E
F
length1
length2
R * length1 = E * lenght2
Effort
force
Engagement
Simple Experiment: Balancing Act
• Using only a meter stick and a wooden block, balance two
masses in a seesaw kind of structure.
• How did you get them to balance?
–
Could you do it in one try?
Do this by
yourself, not in
class
• Compare your setup with other possible setups
This is
useful in
robot arm
design
Exploration
Simple Experiment: Balancing Act
Lever Forces
• Materials
–
–
–
–
–
–
Computer/calculator
Force Probe
500g mass
String
Meter stick
Wooden Block
High school
robotics
Exploration
Lever Forces
Simple Experiment:
Balancing Act
• Measure the Weight of the 500g mass (in Newtons).
• Balance the middle of the meter stick on the wooden block.
• Place the 500g mass at the 90 cm line.
• Attach the string to the meter stick at the 10 cm line.
• Attach the string to the force meter and pull down on the sensor
until the meter stick is balanced.
• Record the force needed to balance the meter stick.
• Repeat the above steps with the 500g mass at the 70 cm line and
the 60 cm line.
Exploration
Simple Experiment: Balancing Act
Lever Forces
• After recording your data in a table, perform
the following calculations for the three trials:
– Divide the weight of the 500g mass by the force
required to balance the meter stick.
– Divide the distance between the force meter
and the wooden block by the distance between
the 500g mass and the wooden block.
• How do these numbers compare?
• What do these numbers indicate about the
lever system?
Explanation
Why use a Simple Machine?
• Simple Machines make work easier by giving the user a mechanical
advantage.
• How do we calculate the mechanical advantage for a lever system?
• Ideal Mechanical Advantage (IMA) = Leffort / Lresistance
• Why do we stipulate that the MA is ideal? Because we’ve assumed that the
machine puts out exactly as much work as we put in. This implies 100%
efficiency
• This situation is never possible…why?
Mechanical
Advantage = MA
Leffort is the distance between the effort force and the fulcrum
Lresistance is the distance between the resistance force and the fulcrum
100% efficiency is never possible because of FRICTION.
Explanation
Lever Example
• A worker uses an iron bar to raise a manhole cover that weighs 90
Newtons. The effort arm of the bar is 60 cm long and the resistance
arm is 10 cm long.
• Draw a picture of this scenario
90 N
• Calculate the IMA of the lever system
IMA = Le/Lr = 60 cm/ 10cm = 6
• What force would the worker need to apply to lift the manhole?
• We need 90 N of force to lift the manhole cover, but we
have a mechanical advantage of 6.
• Now we only need 15 N of force to lift the manhole.
Three
Classes of
Levers
Classes of Levers
“First Class Lever”
• A first-class lever is a lever in
which the fulcrum is located
between the input effort and the
output load.
•
In operation, a force is applied
(by pulling or pushing) to a
section of the bar, which causes
the lever to swing about the
fulcrum, overcoming the
resistance force on the opposite
side.
• The fulcrum may be at the center
point of the lever as in a seesaw
or at any point between the input
and output.
• This supports the effort arm and
the load.
Examples:
•Seesaw
•Scissors (double
lever)
Effort
fulcrum
First Class Lever
Resistance
Fulcrum is between EF (effort) and RF (load)
Effort moves farther than Resistance.
Multiplies EF and changes its direction
The mechanical advantage of a lever is the ratio of the length of the lever
on the applied force side of the fulcrum to the length of the lever on the
resistance force side of the fulcrum.
Examples of first class levers
Common examples
of first-class
levers include
– crowbars,
– scissors,
– pliers,
– tin snips
– and seesaws.
Second Class Lever
Resistance
Effort
RF (load) is between fulcrum and EF
Effort moves farther than Resistance.
Multiplies EF, but does not change its direction
The mechanical advantage of a lever is the ratio of the distance
from the applied force to the fulcrum to the distance from the
resistance force to the fulcrum.
Explanation
Three Lever Classes
• Second class lever
–
–
Resistance is located between the effort force and the fulcrum.
Always multiplies a force
–
Example: Wheelbarrow
R
E
F
Always multiplies a force.
Examples of Second class levers
“Second Class
Lever”
In a second class lever the input
effort is located at the end of the
bar and the fulcrum is located at the
other end of the bar, opposite to the
input, with the output load at a point
between these two forces.
Examples:
•Paddle
•Wheelbarrow
•Wrench
Examples of second-class levers
• Examples of
second-class
levers include:
• nut crackers,
• wheel barrows,
• doors,
• and bottle
openers.
Third Class Lever
EF is between fulcrum and RF (load)
Does not multiply force
Resistance moves farther than Effort.
Multiplies the distance the effort force travels
The mechanical advantage of a lever is the ratio of the distance
from the applied force to the fulcrum to the distance of the
resistance force to the fulcrum
Classes of Levers
“Third Class Lever”
• For this class of levers, the input
effort is higher than the output
load, which is different from
second-class levers and some
first-class levers.
• However, the distance moved by
the resistance (load) is greater
than the distance moved by the
effort.
• In third class levers, effort is
applied between the output load
on one end and the fulcrum on
the opposite end.
Examples:
•Hockey Stick
•Tweezers
•Fishing Rod
Explanation
Three Lever Classes
• Third class lever
–
–
–
Effort force located between the resistance and the fulcrum.
Effort arm is always shorter than resistance arm
MA is always less than one
–
Example: Broom
E
R
F
There is an increase distance moved
and speed at the other end.
Other examples are baseball bat or
hockey stick.
Examples of Third Class Levers
• Examples of
third-class
levers include:
– tweezers,
– arm hammers,
– and shovels.
Third class lever in
human body.
Natural Levers
in Human Body
Elaboration
Natural Levers
• Identify an
example of a
1st class lever
in the human
body
Remember to relax the body
and feel the muscle groups
working to move the bones
Example of first
class lever in
human body
Elaboration
Natural Levers
• Identify an
example of
a 2nd class
lever in the
human
body
Second class
lever in human
body
Remember to relax the body and feel the muscle groups working to move the
bones
Natural Levers
• Identify an example of a 3rd class lever in the human body
Remember to relax the body and feel the muscle
Mechanical Advantage
• Mechanical Advantage is the ratio between
the load and effort.
• Mechanical Advantage deals only with forces.
• Mechanical Advantage > 1 means that the
output force will be greater than the input
force.
– (But the input distance will need to be greater
than the output distance.)
Mechanical Advantage
•First and Second class levers have a positive mechanical
advantage.
•Third class levers have a mechanical disadvantage,
meaning you use more force that the force of the load you
lift.
Velocity Ratio
• Velocity Ratio deals with the distance gained
or lost due to a mechanical advantage.
• Velocity Ration >1 means that the input
distance (or effort) to move a load will be
greater than the output distance of the load.
Mechanical Advantage: Example
Mechanical Advantage =
effort arm
resistance arm
Crazy Joe is moving bricks to build his cabin.
With the use of his simple machine, a lever, he moves
them easily.
The “effort arm” of his wheel barrow is 4ft., while the
resistance arm of his wheelbarrow is 1 ft.
4/1 is his mechanical advantage. MA= 4.
How the Lever changes the
Force?
One convenience of
machines is that you
can determine in
advance the forces
required for their
operation, as well as
the forces they will
exert.
“The length of the effort arm is the same number of
times greater than the length of the resistance arm as
the resistance to be overcome is greater than the
effort you must apply.”
Plugging these into an equation gives you the change
in force by using a lever.
where
L = length of effort arm,
l = length of resistance arm,
R = resistance weight or force, and
E= effort force.
Force Change
• Suppose you want to pry up the lid of a paint can with a 6-inch file scraper, and you
know that the average force holding the lid is 50 pounds.
• If the distance from the edge of the paint can to the edge of the cover is 1 inch,
what force will you have to apply on the end of the file scraper?
L = 5 inches
l = 1 inch
R = 50 pounds, and
E is unknown.
= 10 pounds
• You will need to apply a force of only 10 pounds.
Where can I find levers?
Compound machine:
Can Opener
Simple machines
1. lever
2. wheel and axel
3. gear
4. wedge
There are as many as 4 simple machines in a
stupid CAN OPENER!
Where can I find levers?
Compound Machine:
Stapler
Simple Machines:
-Lever
-Wedge
Every complex
mechanism can be
decomposed to a network
of simple machines
Where can I find compound
machines?
Compound Machine:
Wheelbarrow
Simple Machines:
-Lever
-Inclined Plane
-Wheel and Axel
Wheelbarrow
Levers and Linkages: Conclusions
Concepts
discussed
Understanding of levers and
linkages is important for those
who build robots, especially
humanoids
•
•
•
•
Fulcrum
Load
Effort
Classes
– First
– Second
– Third
Rotary
Mechanisms
Rotary Mechanisms
• Gears, Pulleys, Cams, Ratchets, Wheels, etc.
• These rotary mechanisms transfer of change input
rotational motion and force to output motion and
force.
• Output force can be either rotational or
reciprocating.
rotational motion and force
Rotary
mechanism
rotational or reciprocating motion
and force.
Belts/Pulleys & Chains/Sprockets
• Use belts and chains to convert motion and
force.
• Uses same measures of Mechanical advantage
and Velocity Ratio as gears.
Inclined
Plane
Inclined Plane
– Sloping surface used to lift heavy loads with less effort
http://www.sirinet.net/~jgjohnso/simple.html
Inclined Plane in antiquity
Inclined Plane - Egyptians
• The Egyptians used simple machines to build the pyramids.
• One method was to build a very long incline out of dirt that rose
upward to the top of the pyramid very gently.
• The blocks of stone were placed on large logs (another type of
simple machine - the wheel and axle) and pushed slowly up the
long, gentle inclined plane to the top of the pyramid.
Inclined Plane Principles
• An inclined plane is a flat
surface that is higher on one
end
• Inclined planes make the
work of moving things easier
A sloping surface, such as a ramp. An
inclined plane can be used to alter the
effort and distance involved in doing work,
such as lifting loads. The trade-off is that
an object must be moved a longer
distance than if it was lifted straight up,
but less force is needed.
You can use this machine to move an
object to a lower or higher place. Inclined
planes make the work of moving things
easier. You would need less energy and
force to move objects with an inclined
plane.
• A sloping surface, such as a ramp.
• An inclined plane can be used to alter the effort
and distance involved in doing work, such as
lifting loads.
• The trade-off is that an object must be moved a
longer distance than if it was lifted straight up,
but less force is needed.
• You can use this machine to move an object to a
lower or higher place.
• Inclined planes make the work of moving things
easier.
• You would need less energy and force to move
objects with an inclined plane.
Inclined Plane Mechanical Advantage
• The mechanical advantage
of an inclined plane is
equal to the length of the
slope divided by the height
of the inclined plane.
• While the inclined plane
produces a mechanical
advantage, it does so by
increasing the distance
through which the force
must move.
Work input and output
• Work input is the amount of work done on
a machine.
– Input force x input distance
• Work output is the amount of work done
by a machine.
– Output force x output distance
Wout = Win
Dout
Fout x Dout = Fin x Din
3m
10N x 3m = 2N x 15m
10 N
Din 15 m
Fin
Screw
A screw is an inclined plane
wound around a central cylinder
The mechanical advantage of an screw can be
calculated by dividing the circumference by the pitch of
the screw.
Pitch equals 1/ number of turns per inch.
Screw
– Converts a rotary motion into a forward or
backward motion
http://www.sirinet.net/~jgjohnso/simple.html
Wedges
Wedge
– Converts motion in
one direction into a
splitting motion that
acts at right angles to
the blade
– A lifting machine may
use a wedge to get
under a load
http://www.mos.org/sln/Leonardo/InventorsToolbox.html
Wedges
• Two inclined
planes joined
back to back.
• Wedges are used
to split things.
Wedge – Mechanical Advantage
• The mechanical advantage of a wedge can be found by
dividing the length of either slope (S) by the thickness (T)
of the big end.
S
S/T
T
• As an example, assume that the length of the slope is 10
inches and the thickness is 4 inches.
• The mechanical advantage is equal to 10/4 or 2 1/2.
• As with the inclined plane, the mechanical advantage
gained by using a wedge requires a corresponding
increase in distance.
For Example…
• Assume that the length of the slope (S) of a wedge is
12 inches and the thickness (T) is 3 inches.
• MA = S/T
• MA = 12 inches/3 inches
• MA = 4
How Does a Wedge Change the Force?
• Wedges change the direction of an
applied force.
• When force is applied downward on a
wedge, it distributes the force outward
in two directions, separating a
material.
Example of mechanical advantage
• A box is lifted by two supporting ropes. What
is the mechanical advantage?
• MA=number of supporting ropes
• MA=2
… more examples of …
Compound
Machines
Compound Machine #1
• Bowflex: Pulley lifts the weight, the seat is an
inclined plane, and the lever is what you pull
to adjust the seat
Compound Machine #2
• Crane: The lever is the
horizontal beam that
lifts the object, the
pulley is used to make
the rope tight so that it
is easier for the crane to
lift the object
Compound Machine #3
• Ski Lift: It is an
inclined plane to
travel up a
mountain.
• The pulley is used to
pull the ski lift to the
top of the mountain
Examples of compound machines
A Wedge in a Compound Machine:
Stapler
• Staples are wedges:
they cut through
paper because their
ends are pointed in
a wedge shape.
• There are two simple
machines in a
stapler:
1. Wedge
2. Lever
Examples of compound machines
A Wedge in a Compound Machine: Can Opener
• The cutting edge of
a can opener cuts
through metal
because it is
shaped like a
wedge.
• Simple machines in
a can opener:
–
–
–
–
Wedge
Lever
Gear
Wheel and axle
Examples of compound machines
A Wedge in a Compound Machine: Scissors
• The cutting edge of
scissors is a wedge.
• Simple machines in a
pair of scissors:
– Wedge
– Lever
Questions to
students:
1. Explain the following
concepts
2. Give examples of
each
3. How each can be
used in robotics?
1. Gears
2. Pulleys
3. Chains
4. Cams
5. Bearings
6. Wheel and Axle
7. Inclined Plane
8. Wedge
9. Screw
10. Lever
11. Cranks and sliders
12. Ratcheting mechanisms
13. Clutches
14. Brakes
1. Give definitions of energy, work and force
2. Give examples of these types of motion in robotics:
– Linear
– Reciprocal
– Rotary
3.
4.
5.
6.
7.
8.
Oscillating
What are linkages?
What are the types of linkages?
Give examples of different types of linkages?
What is a lever?
Explain the definitions and give examples of three
classes of levers.
1. Give definition of mechanical advantage
2. Give examples of mechanical advantages in simple
machines such as various classes of levers.
3. Give at least three examples of compound
machines.
4. What are Parallel Linkages, Treadle Linkages amd
Toggle Linkages
5. What is a rotary mechanism?
6. Describe a humanoid arm as a compund machine.
7. The same for a leg
8. The same for a torso
9. The same for a head and neck combination.
Questions.
1. How much effort will be needed to lift a 100
pound load if distance to effort is five feet
and distance to resistance is one foot?
2. How much effort will be needed to lift a 48
pound load if distance to effort is two feet
and distance to resistance is 8 feet?
Project Related
1. Create a kinematic model of your robot
2. Relate it to pulleys, gears, levers,
linkages, etc
3. Perform simple calculations related to
torque, speed and power
Philosophy
• Be able to see and appreciate simple
machines around you
• Be able to steal every idea for your robot.
Bibliography
• http://en.wikipedia.org/wiki/Lever
I got the three types of levers, examples and their functions. (used)
• http://www.tpub.com/machines/1c.htm
I got the formula for mechanical advantage and example. (used)
http://www.edheads.org/activities/simplemachines/frame_loader.htm
I found a list of compound machines and how simple machines were
used in them. (used)
•
http://www.coe.uh.edu/archive/science/science_lessons/scienceles
1/lever.htm
I found examples of levers and how they work.
•
Bibliography
• http://dictionary.reference.com/browse/w
edge
• http://www.uark.edu/depts/aeedhp/agsci
ence/simpmach.htm
• http://www.sciencetech.technomuses.ca/
english/schoolzone/Info_Simple_Machines2
.cfm
• http://www.edheads.org/activities/simplemachines/frame_loader.htm
• http://www.teachervision.fen.com/machines/print
able/45019.html
Bibliography
• http://library.thinkquest.org/27948/pulley.html
– This site explains the use of the pulley system. Also
provides an equation to figure out the force needed to lift
an object with the pulley.
• *http://library.thinkquest.org/J002079F/pulley.htm
– This site defines a pulley and explains how it makes lifting
easier. This site also shows simple examples of pulleys.
• http://www.science.jrank.org/pages/4060/Machines-Simple.html
I used this site to find mechanical advantages, examples, and how a
basic lever works.
Bibliography (Cont.)
*http://en.wikipedia.org/wiki/Pulley
– This site gave the definition of a pulley, different types of pulley
systems, and explains how these systems work.
• http://www.swe.org/iac/lp/pulley_03.html
– This site gives a detailed explanation about pulleys. It shows how it
was invented, by whom it was invented, and provides pictures to show
how a pulley works.
• *http://library.thinkquest.org/CR0210120/MA%20of
%20PS.html
– This site showed how to get the mechanical advantage for a pulley.
Sources
Shawni Yeagley
Nate Yavoich
Raquel y Victoria