Week 2
There are two videos to view this week.
http://www.ted.com/talks/lang/eng/rodney_brooks_on_robots.html
http://www.ted.com/talks/lang/eng/michael_shermer_on_believing_strange_things.html
Robert Brooks shows some interesting robots that he has
built. They demonstrate that there are
fairly sophisticated tasks that robots can perform.
Michael Shermer is a person that
examines claims. Since there are many
astounding claims that people report. It is necessary to evaluate these with a
skeptical perspective. The nature of
science is to carefully analyze data, models, theories and ideas. Science only includes things that can be
tested. A belief therefore falls out of the realm of science.
GSCI 101 9:3010:45 [10:1010:15]
[Force table, spring, ruler (normal force), rope (tension)]
{people pushing and rotating}
Robot
Structure
Consider what this means. First notice that mathematics is a language that provides a concise statement. If you learn the language this type of translation is typically straightforward.
Suppose you find five forces that are acting on our robot structure.
Now lets consider something a bit more difficult. What do the arrows mean?
coordinate systems label POINTS
space
time
Point in space is labeled by three numbers and if it is an event it is labeled by another number time.
(x,y,z) at time t
SCALARS (amount of money, age, number of students in the classroom)
These quantities can be manipulated mathematically to get sums and differences.
Realize that we must add similar quantities. č UNITS
It does make sense to combine different units: rates, speed, …
A point in space is not a simple quantity but a group of numbers. Can we manipulate complex groups. We know the answer. If you are at point A and you need to get to point B can you find the information for the path from the points A, B ?
But now the information is more complex and notice that this complexity can be contained by an arrow. The arrow tells us how far AMOUNT or MAGNITUDE and in which direction. We need to figure out how do we add these more complex entities.
Stand and push. Notice when there is balance. Push same amount but in opposite directions.
Now push on a third person.
Pick an origin. Label some points and show position vectors. Imply that to get to B from A we can think of this as the path generated by moving AčB.
A is the path from out reference point or origin to A
B ‘’’’’’’ B
Graphical Method: (show on board). See appendix C. Further examples can be found online for example at http://en.wikibooks.org/wiki/FHSST_Physics/Vectors/Addition.
ASIDE 
There is a useful trick associated with this idea of the general mathematics. If I know a set of rules and a classic example then perhaps new problems are trivial. Suppose you learn that ten pennies add to 10 that two nickels add to 10 …. Now the problem is if I have ten people how many are there? If I have two families of five how many people are there ? You might look at me and say this is obvious what are you Lets look at a graph of position vs time do flat line then do a sloped line 1 You know a lot already PLEASE USE YOU INFORMATION!!! 2 Get the velocity graph 3 Get the acceleration graph If you can apply the same basic rules to two different things then you only need to figure out these rules once. The application to the second thing will be easy. Method: change the names. Apply the rules. Change the names back. Example: Two families of five becomes to groups of 5 pennies. We know 5 pennies + 5 pennies = 10 pennies Change the names back. 5 people + 5 people = 10 people 
The power of vectors is derived from the fact that many interesting quantities behave in the same manner.
Force, velocity, acceleration, momentum
I always think that these things need to have a “HOW MUCH” and “WHICH DIRECTION” piece.
To complete this discussion two more details:
NEXT LECTURE č finish chapter 1 by introducing speed velocity acceleration.
NEXT WEEK start chapter 2 Newton’s Laws. What is the effect of a force on an object when NOT in balance.
Chapter 1:
Inertial mass
forces čpush or pull
weight (gravity) č well known force (g=9.8 m/ss
which means: magnitude mg, direction down
difference between inertial mass and gravitational mass
Inertial mass measures the resistance to motion. Gravitation mass measures how attracted to bodies are under the influence of gravity. Interesting thing is that they are related. The heavier the object the harder it is to move. Of course you say but if that is your point of view then your missing the argument. The statements above are two independent facts. There is no reason for these two quantities to be related. They are we have intuitively learned this connection and so we assume it is a required connection but it is not. Einstein puzzled over this and found a way within the theory of gravity to link these two facts. 
equilibrium
static č balance small object ∑ forces=0
extended ∑ Torques=0
rotational force is a torque
speed velocity
instantaneous speed
acceleration
Problem
forward and reverse kinematics for
a manipulator.
Forward is you drive the joints and
compute where the hand is.
Reverse is that you choose the goal (
where the hand will go)
There is a complicated process that must be carried out.
Let me just explain a bit to you.
There are ways to express vectors component form (x,y,z). We mentioned this when we
talked about the complexity of a point as an introduction to the need to
introduce vectors.
Lets look at 2 representations of the information in a
vector
Graphical but think length and angle or direction. č
Precise 

3 DOF for a vector č 3 pieces of
information
6 for a rigid body
Discussed rigid bodies, vectors, numbers, types of forces,
equilibrium and graphical addition of forces.
The point is you can introduce other mathematical operations
other than addition.
?? Think of any.
Rotation and translation, stretch.
Rotaions are sweet in that you can
build a rotation matrix and use a new form of multiplication to arrive at the
rotated vector
GSCI 101 9:3010:45
[10:1010:15]
[Force table, spring, ruler (normal force), rope (tension)]
{people pushing and rotating}
Review
Robot
Structure
Consider what this means.
First notice that mathematics is a language that provides a concise
statement. If you learn the language this type of translation is typically
straightforward.
Suppose you find five forces that are acting on our robot
structure.
end of review
Force table
If you can identify all of the forces acting on an object at
rest and you sum them up using the vector nature of forces then you can ask if
the sum is zero or non zero. The non zero case puts the body in
equilibrium [ignoring the most general case of extended objects which still can
twist and turn even when the total force is zero]. The result is that the object remains at
rest. ROBOT DOES NOT FALL DOWN.
Is there an easy way to balance forces so that our robot
doesn’t fall?
Build it like a car
Forces to know
[Unit of force is the Newton] 

gravity 
mg down 
Support force or Normal 
Automatic force of a surface [away from the surface] 
Friction 
Force
that resisits motion [surface may
exert along its sur.] 
Net 
Vocabulary word for the total force 
Spring force 
Force that a compressed or stretched spring exerts 
Air resistance 
Type of frictional 
Tension 
Stretching force that ropes exert 
Tension is a complicated phenomena. Sometimes it is easier to examine ropes
used to support or pull something [under dynamic equilibrium or balance] At each point the rope is pulled equally in both directions. The amount or magnitude of this pull is the tension. Tension is the amount of force applied to the end. For balance each end must have a force equal to the
tension applied. Rope forces act along the direction of the rope. A pulley or person (on a rope swing). Feels forces equal
to the number of contacts to the rope. (On the swing imagine that your hands
are supporting you and then you see that each hand will feel a rope force
up.) 
NEXT LECTURE č finish chapter 1 by introducing speed velocity acceleration.
NEXT WEEK also start chapter 2 Newton’s Laws. What is the effect of a force
on an object when NOT in balance.
Chapter 1:
Inertial mass
forces čpush or pull
weight
(gravity) č
well known force (g=9.8 m/ss
which means: magnitude mg, direction down
difference between inertial mass
and gravitational mass
Inertial mass measures the resistance to motion. Gravitation mass measures how attracted to bodies are
under the influence of gravity. Interesting thing is that they are related. The heavier the object the harder it is to
move. Of course you say but if that is
your point of view then your missing the argument. The statements above are two independent facts. There is
no reason for these two quantities to be related. They are we have intuitively learned this
connection and so we assume it is a required connection but it is not. Einstein puzzled over this and found a way within the
theory of gravity to link these two facts. 
equilibrium
static č balance small object ∑ forces=0
extended ∑ Torques=0
rotational force is a torque
speed velocity
instantaneous speed
acceleration