Hi Guys,
I am planning to make a small articulated arm type small robo for learning purpose. My robo will have two arms pin jointed together and the first arm is also pin jointed to the base the base can rotate about vertical axis

.
. r2
.
. pin joint
. /
. /
. /r1
........../pin joint
---------------------------
--------base can rotate----

The lengths of the arm are r1 and r2 respectively. Thus in this case if the base of robo is considered origin then the tip of r2 arm is at point.
x=(r1*cos(a)+r2*cos(c+a-180))*cos(b)
y=(r1*cos(a)+r2*cos(c+a-180))*sin(b)
z=(r1*sin(a)+r2*sin(c+a-180))

where a is the angle r1 makes with ground. b is angle through which base rotates and c is the angle that r2 makes with r1.
now, In my case x,y,z will be known then if i use servo motors to give rotation a,b,c. I will need equation for a,b,c= F(x,y,z) so that I can determine these angles and give appropriate rotaion to make tip of r2 arm point to point (X,Y,Z) in space. so far I have been able to find equation for b only.
b= tan-1(y/x) I still dont know how to get equation for a & c. If anyone of you guys have ever worked with such a situation let me know what to do.
Thanks for reading...