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Topic: arm and upper arm of robot
Replies: 1   Last Post: Oct 16, 2013 7:16 AM

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 Torsten Hennig Posts: 2,419 Registered: 12/6/04
Re: arm and upper arm of robot
Posted: Oct 16, 2013 7:16 AM

> Helllo everyone!!
> Please help me to do a program of this picture
> http://axgig.com/images/46945497046900351711.jpg
> Please I need help!
> Input=(x,y)
> Output
> a=?
> b=?

1. Square the equations for x and y:
x^2 = c^2*cos^2(a)+d^2*cos^2(b)+2*c*d*cos(a)*cos(b)
y^2 = c^2*sin^2(a)+d^2*sin^2(b)+2*c*d*sin(a)*sin(b)
2. Add both equations:
x^2+y^2=c^2+d^2+2*c*d*cos(a-b)
3. Solve for (a-b):
cos(a-b)=((x^2+y^2)-(c^2+d^2))/(2*c*d)
a=b+acos(((x^2+y^2)-(c^2+d^2))/(2*c*d))
4. Insert the expression for a:
x=c*cos(b+m)+d*cos(b)
with m = acos(((x^2+y^2)-(c^2+d^2))/(2*c*d))
5. Using
cos(b+m)=cos(b)cos(m)-sin(b)sin(m), you get
x=c*(cos(b)cos(m)-sin(b)sin(m))+d*cos(b)
or
x=cos(b)*(c*cos(m)+d)-sin(b)*c*sin(m)
6. Replace cos(b) by sqrt(1-sin^2(b)):
x+sin(b)*c*sin(m)=sqrt(1-sin^2(b))*(c*cos(m)+d)
7. Squaring both sides of the last equation
leads to a quadratic equation in sin(b).
Solve this equation for sin(b) and thus b.
8. Use
a=b+acos(((x^2+y^2)-(c^2+d^2))/(2*c*d))
to get a.

Best wishes
Torsten.

Date Subject Author
10/15/13 Afshin
10/16/13 Torsten Hennig