The kinematic synthesis of serial manipulators with a prescribed Jacobian

The authors address the kinematic synthesis of serial-type robotic manipulators under the assumption that the associated Jacobian matrix is prescribed at a key configuration. By recalling that the columns of the Jacobian matrix are the Plucker coordinates of the joint axes and using a dual unit vector representation of these lines, the manipulator synthesis, i.e., the determination of the underlying architecture, is obtained. Examples of the application of the synthesis method to isotropic redundant manipulators are given.>