inverse-kinematics

I am trying to implement Inverse Kinematics on a 2D arm(made up of three sticks with joints). I am able to rotate the lowest arm to the desired position. Now, I have some questions: How can I make the upper arm move alongwith the third so the end point of the arm reaches the desired point. Do I need to use the rotation matrices for both and if yes can someone give me some example or an help and is there any other possibl;e way to do this without rotation matrices??? The lowest arm only moves in one direction. I tried google it, they are saying that cross product of two vectors give the

Lets say I've a robotic arm with joints at points A,B,C,D in a 3D space. Let D be the end effector(bottommost child) and A be the topmost parent. Let T be the target point anywhere in the space. The aim is to make the end effector reach the target with minimum rotations in top levels(parents). What I initially thought: 1) Rotate the arm C by angle TCD. 2) Then rotate the arm B by new angle TBD. 3) Then rotate the arm A by new angle TAD. But the end effector seems to point away from the target after step 2. What am I doing wrong and how can I fix it? It's hard to directly code this, but you may