In the field of robotics, there is a necessity to calculate the 3D position and orientation of the end-effector given full or partial information on the orientations and positions of the links ; such calculations often have to be performed quickly. A more difficult task is to determine the positions and orientations of the intermediate links necessary to achieve a final given configuration of the end effector. For this latter task the solutions can be either unique, non-existent or multiple, depending upon the constraints in the kinematic chain. Finding solutions, which are known to be unique, by the conventional methods generally proceed along somewhat ad-hoc lines and employ restrictions on joint angles to avoid singularities which are introduced by the method of solution. Here we will present a systematic method of solving the inverse kinematics which avoids the occurrence of these singularities -- the method uses the geometric algebra framework and will be illustrated on a 3 link insect leg configuration as employed in many hexapod walking robots. We will also indicate how the unified framework provided by geometric algebra enables us to incorporate the dynamics of the robot into the method and illustrate its possible uses in robotic control.

jl@eng.cam.ac.uk