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MathGroup Archive 2006

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Re: Re: Re: Solve or Reduce?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64453] Re: [mg64412] Re: [mg64398] Re: Solve or Reduce?
  • From: Math Novice <math_novice_2 at yahoo.com>
  • Date: Fri, 17 Feb 2006 04:12:31 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

  Thank you all for your responses. I have a lot to learn about using Mathematica but it should be a very interesting process. What I am trying to do with this problem is to try and understand how an automobile?s double wishbone suspension determines the orientation of the wheel?s plane as the suspension moves. I need to be able to rotate three non collinear points, say, (13,0,0), (13,3.5,0) and (13, 3.5,3.5) an arbitrary number of degrees (corresponding to the movement of the suspension) and then use these three new points to determine the orientation of the wheel?s plane so that I can graph the movement. I?ve already done this for a semi-trailing arm suspension which basically just required rotating three points in the wheel?s plane about an arbitrary axis. I want to be able to see visually why the more modern double wishbone and multilink suspensions are superior to the older suspension designs.


David Park <djmp at earthlink.net> wrote:  The following table gives the solutions in degrees as a varies from 0 to 90
degrees. Each triplet is {a, first b solution, second b solution}. Because
the RootSearch routine I was using gives the results in sorted order, the
two roots switch columns at 60 degrees.


{{0, 0., 277.628},
{5, 8.14157, 279.009},
{10, 16.3816, 281.034},
{15, 24.8218, 283.798},
{20, 33.5778, 287.445},
{25, 42.7897, 292.171},
{30, 52.6316, 298.233},
{35, 63.3125, 305.928},
{40, 75.0545, 315.54},
{45, 88.0132, 327.201},
{50, 102.111, 340.683},
{55, 116.839, 355.264},
{60, 9.92425, 131.266},
{65, 23.8027, 144.4},
{70, 36.4951, 155.625},
{75, 47.9915, 164.805},
{80, 58.473, 172.123},
{85, 68.1628, 177.873},
{90, 77.2632, 182.348}}

There are always two solutions and they are perfectly well behaved.

Those who have the Cardano3 complex graphics package, and Ted Ersek's
RootSearch package and who are interested in the solution, and animations of
the solution, may contact me and I will send them the solution notebook,
CirclesGeometry.nb.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

From: Math Novice [mailto:math_novice_2 at yahoo.com]
To: mathgroup at smc.vnet.net


I am trying to find the angle b corresponding to the points on the
circumference of the circle (5+8 Cos[b], 7+8 Sin[b]) that are a distance of
7 units from a point on the circumference of the circle (13 cos[a], 13
Sin[a]) for angles a in the first quadrant. (5+8 Cos[b], 7+8 Sin[b]) is a
circle of radius 8 and center (5,7) and (13 cos[a], 13Sin[a]) is a circle of
radius 13 and center (0,0).

(13,0) on the circle (13 cos[a], 13 Sin[a]) and (13,7) on (5+8 Cos[b], 7+8
Sin[b]) are the first set of points that are 7 units apart when the angle a
(of the larger circle ) is equal to 0. As I increase the value of a and use
my compass (set at 7 units) to measure on the printout of the diagram of the
two circles it seems that there should always be an angle for b that
corresponds to a and b should always increase as a increases but something
happens at about 32 degrees. For some calculations b starts to decrease as a
increases past 32 degrees or with some other calculations b becomes negative
as a increases past 32 degrees. Any idea of what I'm going wrong?



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