Abstract:

Conformal geometric algebra (CGA) and Dixon resultant are introduced to the inverse kinematics analysis of the serial mechanisms and to the inverse solution of the general 6R robot. First, it shows that homogeneous transforms matrix in terms of CGA will lead to CGA form kinematics equations of 6R robot; Second, the resultant is obtained by using linear elimination and Dixon elimination to eliminate 5 variables; Finally, a 16th degree equation containing a variable is properly derived from the resultant. This algorithm also can be applicable to the inverse kinematics analysis of the robots with 16 roots such as 7R, 1P5R and 4R1C, so it has universal usage.

Key words: Conformal geometric algebra (CGA), Dixon resultant, 6R robot, inverse kinematics analysis