Mapping of kinematic and dynamic parameters for coupled manipulators

Industrial manipulators use various types of transmissions, such as gears, belts, chains, and parallel mechanisms, to transmit driving power to the links. By arrangement many such transmissions cause coupled joint motions. Manipulators having coupled joint motions are referred to as coupled manipulators. Conventional methods for constructing Jacobian matrix and compliance matrix are not directly applicable to coupled manipulators. The concept of the mapping matrix is used in this paper for establishing relationships of torque, speed, Jacobian and compliance of these manipulators with those obtained with conventional methods. A method of constructing the mapping matrix systematically is discussed. Two examples show that the proposed method is easy to implement.