Go Premium for a chance to win a PS4. Enter to Win

x
?
Solved

Reversing the Kiwi-Drive formula

Posted on 2011-02-25
3
Medium Priority
?
534 Views
Last Modified: 2016-05-20
We've recently build a kiwidrive robot, and now we want to use it as a musical instrument.
It has three wheels, each with a motor that produces a distinct tone.
The formulas used to calculate motor speeds are as follows:

M1 = 0.5 * X - 0.866 * Y + R
M2 = 0.5 * X + 0.866 * Y + R
M3 = X + R

Since we are no good at math, we need help reversing these formulas so that for a given M1, M2 and M3, we want to calculate X, Y and R.

Thanks!
0
Comment
Question by:JasonMewes
  • 2
3 Comments
 
LVL 44

Accepted Solution

by:
Arthur_Wood earned 2000 total points
ID: 34978990
solveing the three equations, for the three unkowns (X,Y and R)

R =  0.5 * M1 + 1.5 * M2 - M3
X = -0.5 * M1 - 1.5 * M2 + 2* M3
Y = (1/1.732)*(M2 - M3)

do you need to see the details?

AW


0
 

Author Comment

by:JasonMewes
ID: 34979544
Didn't look quite right, so I double checked:

x = 50, y = 12, r = 97

M1 = 0.5 * x - 0.866 * y + r
M2 = 0.5 * x + 0.866 * y + r
M3 = x + r

r = 0.5 * M1 + 1.5 * M2 - M3
x = -0.5 * M1 - 1.5 * M2 + 2 * M3
y = (1 / 1.732) * (M2 - M3)

yields: x = 39.608, y = -8,43418013856813, z = 107,392

In any case my initial formula was wrong but I would have given you your points anyways if the answer had been correct, but as demonstrated above it doesn't seem to be. Correct me if I made a mistake.

The correct formula should have been:

M1 = -0.5 * X - ( sqrt( 3 ) / 2 ) * Y + R
M2 = -0.5 * X + ( sqrt( 3 ) / 2 ) * Y + R
M3 = X + R

For which the solution seems to be:

X = ( -2 * M3 + M2 + M1 ) / -3
Y = ( M1 - M2 ) * ( sqrt( 3 ) / -3 )
R = ( M3 + M2 + M1 ) / 3

Points to anyone who can verify the validity of the solution.
0
 
LVL 44

Expert Comment

by:Arthur_Wood
ID: 34981319
the original question stated:

M1 = 0.5 * X - 0.866 * Y + R
M2 = 0.5 * X + 0.866 * Y + R
M3 = X + R



now you indicate that the 'correct' formula should have been

M1 = -0.5 * X - ( sqrt( 3 ) / 2 ) * Y + R
M2 = -0.5 * X + ( sqrt( 3 ) / 2 ) * Y + R
M3 = X + R

notice the sign difference on the first factor of M2.

with the new formulae,

M1 +M2 = -X + 2 * R
M3 = X + R

hence R = (M1 + M2 + M3)/3

X = - (M1 + M2) + 2 *(M1 + M2 + M3)/3 = (2 * M3 - M1 - M2)/3 (which is the same as  ( -2 * M3 + M2 + M1 ) / -3)

Y = (M2 - M1) /sqrt(3) = (M2 - M1) * Sqrt(3)/3  which is the same as  ( M1 - M2 ) * ( sqrt( 3 ) / -3 )


AW
0

Featured Post

Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Article by: evilrix
Looking for a way to avoid searching through large data sets for data that doesn't exist? A Bloom Filter might be what you need. This data structure is a probabilistic filter that allows you to avoid unnecessary searches when you know the data defin…
Aerodynamic noise is the cause of the majority of the noise produced by helicopters. The inordinate amount of noise helicopters produce is a major problem in the both a military and civilian setting. To remedy this problem the use of an aerogel coat…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Suggested Courses

963 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question