The Design of Open-Loop Manipulator Arms With Decoupled and Configuration-Invariant Inertia Tensors

A manipulator design theory for reduced dynamic complexity is presented. The kinematic structure and mass distribution of a manipulator arm are designed so that the inertia matrix in the equation of motion becomes diagonal and/or invariant for an arbitrary arm configuration. For the decoupled and invariant inertia matrix, the system can be treated as a linear, single-input, single-output system with constant parameters. Consequently, control of the manipulator arm is simplified, and more importantly, the reduced dynamic complexity permits improved control performance. First, the problem of designing such an arm with a decoupled and/or configuration-invariant inertia matrix is defined. The inertia matrix is then analyzed in relation to the kinematic structure and mass properties of the arm links. Necessary conditions for a decoupled and/or configuration-invariant manipulator inertia matrix are then obtained. Using the necessary conditions, the kinematic structure and mass properties are found which reduce the inertia matrix to a constant diagonal form. Possible arm designs for decoupled and/or invariant inertia matrices are then determined for 2 and 3 degree-of-freedom manipulators.