Generalized solution for a sub-problem of inverse kinematics based on product of exponential formula

Inverse kinematics presents nontrivial problems in serial manipulators as there is no unique, generalized solution that is applicable to various configurations. Till date, limited results exist on skew configurations, while the published problem definitions and solutions are physically nonintuitive. We present a generalized solution for a subproblem of inverse kinematics based on an exponential formula product, in accordance to a geometrically intuitive method. A case study with a six-degree-of-freedom manipulator is presented to verify the effectiveness of the proposed definition and solution. The latter can be adopted to analyze inverse kinematic problems applicable to various serial manipulators.