Inverse Kinematics of Six-Joint Special Manipulators

This work provides a solution to the inverse kinematics problem of special six-joint manipulators using the algebra of dual quaternions and techniques in algebraic geometry such as the Grobner basis and multi-dimension analysis of varieties in the seven-dimensional projective space. Unlike general six-joint manipulators, special manipulators have the property that the workspace of the left or the right 3-chain lies entirely in the Study quadric. It is found that desirable finite inverse kinematics solutions depend on the nature of the computed hyperplane pencils or fixed linear spaces that contain the workspaces of the 3-chains. Algorithms are provided to outline the procedure when the workspaces are contained in a pencil and a linear space in the quadric. To illustrate, we provide an example of a special manipulator and solve its inverse kinematics solutions.