Subject:
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Re: positioning of robot
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lugnet.robotics.handyboard
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Date:
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Sat, 16 Aug 1997 20:52:22 GMT
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root <ROOT@SNOTNOSE.WIZARDstopspam.ORG>
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First, my appologies that this posting is off the mailing list's intended
topic (the HandyBoard) but as it seems to be drawing a lot of interest I
am hoping that continuing it is ok with everyone?)
> I had some questions regarding John Whitten's recent posting about different
> drive types.
>
> > 4 WHEELS:
> > However, the 4 Wheel mechanism also has some disadvantages as well.
> > The biggest problem you will have using a 4 Wheel vehicle is in
> > navigation. A 4 Wheel vehicle has a minimum turning radius. [...]
Ok- first a disclaimer - I am not an engineer- (I don't even play one on TV)
I am just a hobbyist like many of the rest of us- so everything I say may be
a lie... or it may not :) Caveat Emptor, Your mileage may vary, E. Plurabis
Unum, and other legal junk... Also I'll take a moment to hawk my web page at
http://www.vnet.net/wizorg which contains more information about robotics,
68HC11's (especially links), my implementation of a HandyBoard compatible
controller (the Gadget Board) with different I/O specs, some of my robotics
experiments, etc... if you want to check it out. Also another really good
resource is Roger Arricks' robotics web page at http://www.robotics.com. Both
pages (his and mine) have lots of useful links to other places.
That being said- the first thing that any serious robotics hobbyist should
do (IMO) is go dredge up a copy of a book:
"ANDROID DESIGN Practical Approaches for Robot Builders"
by Martin Bradley Weinstein
Hayden Books 1981 ISBN: 0-8104-5192-1
I think this book is now out of print (someone else may know better??) but
if all else fails you should be able to obtain a copy at your library- perhaps
through the Inter-Library Loan program.
While the book is a little dated at this point (it having been published in
1981 and all) it is surprisingly relevant overall. Most of the fundamental
problems of mechanics have changed very little since 1981 though some of the
electronic circuits that are referred to are getting a little stale.
The book isn't so much of a "here's how you build it" book as much as it is
a collection of discussions about interesting problems and challenges facing
the robot designer. It has lots and lots of cool information in it. I very
heartily recommend it!
I am going to blatently swipe some relevant portions from this book here to
help answer some of these questions. If Mr. Weinstein or Hayden Books has
any objections, they can bloody well re-issue the book :)
Before addressing your questions- let me quickly run through the table of
contents in the book so you can get an idea of what all it contains (I don't
normally do book reviews but this one merits an exception :)
Android Design: Table of Contents [annotated by me]
1. Why are you reading this book?
Talks about why you want to build a robot, getting your
design goals thought out before getting started, general
areas of contention, etc.
2. Defining Terms
Obvious
3. The End
A brief discussion about the end product and what your
expectations should be.
4. Philosophical Considerations
How people and robots will interact, etc (brief chapter)
5. Obstacles in the Human Environment
Good chapter on obstacles, how to define them, how to
classify them, what to do about them, etc.
6. The special problems of stairways
obvious
7. Designing the main mechanical drive
A very good discussion regarding exactly what we've been
discussing on this mailing list recently, and what I'll
get into next.
8. The chassis
Talks a lot about building the central structural components
of a robot. Goes into suspension, shock-absorption, weight,
materials, etc.
9. The Main Motor Drive
Defines and discusses motors (mainly DC motors) in general.
10. The Battery
Lots of good, useful (and still topical) information about
batteries, charging systems, power consumption, etc. This
is a very FUNDAMENTAL (in fact, in my opinion THE most)
issue involved in robotics!
11. Motor Juice Concentrate
A really good chapter covering types of motors, how they
work, their power characteristics, precision, etc. Lots of
information you can use right away.
12. The "Other" Motors
Finishes the discussion begun in the previous chapter and
gets into stepper motors and servos and such.
13. Taking the heat off
Talks about getting rid of excess heat (probably should be
covered earlier along with the other power stuff- but who
cares? its here now :)
14. Collision avoidance
Probably should have been discussed earlier near the obstacles
chapter- but in any case- gives a good discussion regarding
the problems involved in object detection, some ideas about
implementation, etc
15. Fingers
A good chapter with interesting ideas about how to design
and build 'end effectors'.
16. Vision by Ramera
Talks about a wacky idea that some people played around with
for robotic vision in the late 70's (back when RAM chips still
had a 'lid' on them)
17. Mapping, the Atlas, and Probability Shells
Gets into navigational considerations
18. Voicebox
Pretty dated information about speech synthesizer products
of 1981 vintage
19. Verbal Literacy
A very interesting beginning into NLP (Natural Language
Parsing/Processing)
20. Brains
Continues from the previous chapter and gives an introduction
to some AI concepts (again 1981 vintage).
21. Letters
Feedback from people the author has corresponded with which
contains interesting questions or points of clarification.
22. The beginning
This is a "Now that you've read through the book, where should
I start?" type of chapter
> How is the math to figure out the narrowest space a vehicle can turn around
> in done? (What formula -- or formulas -- are used? Don't just give names,
> please, include the formula and an explanation of the variables.) This is
> something that I need to consider in my current project, and if I can have
> some idea of how narrow the space is, I can adjust my design as needed,
> rather than redesigning it if it doesn't turn narrow enough.
Ok- the first thing you need to know is the absolute turning radius of your
vehicle. This assumes that the vehicle can turn on its own center:
Turning_Radius = SquareRootOf( ( ( MaxLength ^ 2 ) / 2 ) + ( MaxWidth ^ 2 ) )
MaxLength and MaxWidth are the (squared-off) dimensions of the vehicle.
I don't know of an easy formula to determine the turning radius for a 'car-
like' vehicle (maybe someone else does? Some sort of spiral function maybe?)
but I can tell you about a simple empircal measurment you can make to find
out- position your vehicle with its wheels straight and mark underneath the
center of the vehicle. (If you don't already have a vehicle, do it with a
piece of cardboard and then scale it later to match the dimensions of your
real vehicle) Then turn fully (left or right, doesn't matter) and move
(forward or reverse) and pay attention to when the vehicle _fully_ enters
its turning circle. At that moment, again mark underneath at the outside-
center of the vehicle. Draw a line between the two points you've marked
and that should be a very close approximation to its actual turning radius.
> > This has implications on traction, top-speed, power-input/speed-output
> ratio, and handling (while steering for instance).
>
> What is top-speed?
Top-speed is dependent mainly on the amount of power (torque) you have
available at the wheels, the size of the wheels, with a coefficient for
the drag (based on the surface area in contact with the ground).
(quoted/paraphrased freely from the main motor drive section)
Rotational/Linear Speed Ratio. This equation relates the rotational speed
of the wheel to the linear speed of the vehicle. The variable 'D' is the
diameter of the wheel in question:
Revolutions feet 60 seconds 1 revolution 12 inches
----------- = ------ * ---------- * ------------- * ---------
minute second 1 minute pi * D inches 1 foot
Revolutions feet 60 x 12
----------- = ------ * -------
minute second pi * D
Revolutions feet 1
----------- = ------ * 229.2 * -
minute second D
So if your vehicle were moving along at 2 feet/second (1.3 mph) and its
wheels were 10 inches in diameter, your motor (final drive gear, whatever)
would be turning at 45.8 rpm.
Torque describes the 'twisting force' applied over a distance. It can be a
lever, a wheel, or anything that is free to rotate around an axis or fulcrum
point. The amount of force and the amount of distance determine the amount
of torque:
Torque = force * distance
The usual units of torque are inch-ounces, inch-pounds, and foot-pounds
meaning the amount of "ooomph" it requires to move a unit of weight by a
unit of distance. Weight is a primary consideration in determining how
much torque is required at the motor. Other forces (drag) are also present.
Then the acceleration required must be considered (how soon will it take
for it to go a given speed). Torque does not vary with speed. However it
does with acceleration as the motor approaches it's no-load point. In
order to calculate the force you'll need to know the weight of the vehicle
adjusted for pound units by cancelling out the gravitational factor (32
feet per second per second- 32 ft/second^2). The force required to move
(without climbing) a mass of a specified weight is:
Weight
Force = ------- * acceleration
Gravity
Stealing from the book- this turns out to be 3.1 pounds per 100 pounds of
weight at an acceleration of 1 foot per second per second (1ft/second^2)
or 6.2 pounds per 100 pounds of weight at 2ft/second^2. To put that into
more common terms, 1ft/second is just a little over 1/2 mph. A person's
normal walking speed is typically around 2 mph. A typical average car (say
getting on a highway) accelerates from zero to sixty mph in around 6 to 8
seconds.
Finally, by converting the speed and torque into 'horsepower' which is
defined as:
Speed * Torque
Horsepower = --------------
63,000
You can begin to relate a particular motor (characterized by its torque)
to the vehicle speed modulated by the weight of the vehicle and the required
acceleration.
As for the traction/drag/friction issue that involves a lot of things like
the width of the wheel, the material of the wheel, the type of ground being
covered, the speed of the vehicle, its velocity, angle of momentum and all
sorts of things. Perhaps someone else would like to tackle all that, I'm
worn out- As for traction though, sum it up as Nehuck zindabar (wider is
better :)
I think that covers all the math- somebody holler if I left something out...
> > TREADED OR TRACKED DESIGNS:
> >
> > If the mechanism is not well suspended, or the shock absorption system
> > is lacking (or not there!) or the load-point calculations are off (or
> > were never done), etc, etc, the resulting vehicle will have its
> > lifespan, range, power, speed, durability, handling, load-capacity,
> > etc affected significantly!
>
> What are load-point calculations? What sort of formulas are used with them?
> (Again, I would prefer the formula itself rather than a name.) What sort of
> things make up shock absorption systems? Where would one be implemented?
> (Note: I know nothing about cars, telling me to examine one will not help at
> all...I know cars have some sort of shock absorption system, but that's about
> it.)
What I mean by load-points are the areas of the frame and the internal-joined
areas of the track assemblies that will need to carry the weight of the
vehicle as well as survive the additional forces that will be applied in its
operation (weight will cause stress, bouncing and moving will create strain
and sheer forces, running into things will unleash additional sources of
forces). In a wheeled vehicle you have similar considerations of course.
Also there is the (arbitrarily derived) maximum allowable force for the
contents of the vehicle (cameras, electronics, whatever). This implies
suspension.
By using suspension of various types you can alter the dynamics of how your
vehicle responds to these force elements. If you have a vehicle of a given
weight and 4 wheels, each of those wheels will carry some portion of the
load. How much will depend on where they are located in relation to the body,
the distribution of mass within the body, and so forth. This is really a
whole area in physics I think- and probably a lot more than you (or I :)
want to wade through in one posting.
Here is a brief example describing a picture suspended by wires, (from one of
my old physics books). This is not exactly the same problem but it is similar
enough I think to get the idea across-
"A picture weighing 8 N is supported by two wired of tension T1 and T2, find
the tension in the wires". [The accompaying figure illustrates a level board,
and two wires- T1 is 60deg (with respect to the board) and T2 is 30deg.] Since
the picture does not accelerate, the net force acting on it must be zero. The
three forces acting on the picture- its weight (mg), the tension T1 in one
wire, and the tension T2 in the other- must therefore sum to zero... Since
weight only has a vertical component (mg downward), the horizontal components
of the tensions T1 and T2 must balance each other, and the vertical components
of the tensions must balance the weight:
SUM(Fx) = T1 * cos(30deg) - T2 * cos(60deg) = 0
SUM(Fy) = T1 * sin(30deg) - T2 * sin(60deg) - 1mg = 0
Using cos(30deg) = SquareRootOf(3/2) = sin(60deg), and, sin(30deg) = 1/2 =
cos(60deg) and solving for the tensions, we obtain:
T1 = 1/2mg = 4 N
T2 = SquareRootOf(3 * T1) = (SquareRootOf(3)/2)mg = 6.93 N"
[end quote]
If you want a more detailed answer than that, I suggest you find a good text
on mass and motion.
> Thanks for your help, in advance.
>
> -Kate Rasing
> krasing@iastate.edu
> Chemical Engineering
Hope this helps- and I also hope nobody yells too much for it being so much
off the 'HandyBoard' topic. :)
John Whitten
brat@naxs.com
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