Inverse kinematics and geometric singularity analysis of a 3-SPS/S redundant motion mechanism using conformal geometric algebra

• We propose a 3-SPS/S redundant motion mechanism with kinematic redundancy.
• We define a cost function for fast manipulation of the proposed mechanism.
• We propose an optimization process for obtaining the optimal solution using geometric approaches.
• We have implemented a study to analyze and avoid singularities by using CGA.

We propose a 3-SPS/S redundant motion mechanism with kinematic redundancy in this paper. The proposed mechanism with redundancy enables redundant motion as it works like pan/tilt systems to reduce the unnecessary degree of freedom for the yaw and pitch motions in the configuration space. By reducing one degree of freedom, this robot has self-motion that causes the inverse kinematics to have infinite solutions, so that the proposed research performs an optimization process for obtaining the optimal solution using geometric approaches. This optimal solution provides the fastest response among the infinite solutions by minimizing each link movement to the target orientation. In addition, we perform a geometric singularity analysis due to limited link length and avoidance using conformal geometric algebra for the feasibility and correctness of the inverse kinematics.