On the Dynamic Properties of Rigid-Link Flexible-Joint Parallel Manipulators in the Presence of Type 2 Singularities

In our previous work (2008, “Optimal Force Generation in Parallel Manipulators for Passing through the Singular Positions,” Int. J. Robot. Res., 27(8), pp. 967–983), the dynamic properties of rigid-link parallel manipulators, in the presence of type 2 singularities, have been studied. It was shown that any parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition was obtained using the symbolic approach based on the inverse dynamics and the study of the Lagrangian of a general rigid-link parallel manipulator. It was validated by experimental tests carried out on the prototype of a four-degrees-of-freedom parallel manipulator. However, it is known that the flexibility of the mechanism may not always be neglected. Indeed, joint flexibility is the main source contributing to the overall manipulator flexibility and it leads to the trajectory distortion. Therefore, in this paper, the condition for passing through a type 2 singularity of parallel manipulators with flexible joints is studied. The suggested technique is illustrated by the example of a 5R parallel manipulator with flexible joints. It is shown that passing through singularity is possible if the 12th-order polynomial trajectory planning is applied. The obtained results are validated by the numerical simulations carried out using the ADAMS software.