Study of the robotic manipulators´ kinematic manipulability

The series robotic manipulator´s operation space is studied, the conclusion that the greater of the robotic manipulator´s operation space volume, the better of the robotic manipulator´s manipulability is drawn, volume element based on redundant robotic manipulator´s kinematics is proposed as an operational performance index. ⁿ-DOF serial robotic manipulator´s operation space is ⁿ-dimensional Riemannian manifold, the ⁿ-dimensional Riemannian manifold volume is calculated using the moving coordinate system and the exterior product definition in differential geometry, and get the robotic manipulator´s operation space volume, and compared the obtained results with the operation space volume using inner product determinant in the literature, it shows that the volume element as a kinematic operational performance index is feasible.