Abstract:

To obtain the translational parallel mechanism with constant Jacobian matrix, a method solving Jacobian matrix of mechanism using main movement screw and transmission wrench screw is proposed based on screw theory. Some determination conditions in a translational parallel mechanism requires to keep its Jacobian matrix constant in different poses are presented. On this basis, a class of 3-DOF translational parallel mechanisms each limb of which has three, four and five joints with the above characteristic is synthesized based on screw theory. Many different translational parallel mechanisms with constant Jacobian matrix are obtained. By taking the 3-PPRU and 3-CPU translational parallel mechanism as examples, the Jacobian matrices of the mechanisms are analyzed. According to the former analysis, graphs of time-rate change of the output speed and force for the mechanisms in different poses are presented. It can be seen from the graphs that the curves of the same output parameters for the mechanisms will mutual coincide in different poses with the certain input parameters. Thus, the conclusion that Jacobian matrix of the class of translational parallel mechanisms keeps constant is verified.

Key words: Jacobian matrix, translational parallel mechanism, type synthesis, screw theory