On the dynamic properties and optimum control of parallel manipulators in the presence of singularity

Abstract

It is known that a parallel manipulator with a singular configuration can gain one or more degrees of freedom and become uncontrollable. That is it might not reproduce a stable motion under a prescribed trajectory. However, it is proved experimentally that there is possible passing through the singular zones. This was simulated and shown on numerical examples and illustrated on several parallel structures. In this paper, we determine the optimal dynamic conditions generating a stable motion inside the singular zones. The obtained results show that the general condition for passing through a singularity can be defined as follows: the endeffector of the 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 is obtained from the inverse dynamics and analytically demonstrated by the study of the Lagrangian of a general parallel manipulator. Numerical simulations are carried out using the software ADAMS and validated by experimental tests.

Planning Singularity-Free Paths on Closed-Chain Manipulators

“…Many types of singularities can be distinguished [11], but those of primary interest in this paper are the direct or forward singularities, which compromise the velocity control of a manipulator, leading to malfunction or a breakage of the structure. Unless the use of involved control strategies would be affordable [12,13], any path connecting two configurations should avoid crossing such critical configurations. In many contexts, moreover, a minimum clearance with respect to the singularity locus should be maintained, to avoid the negative effects of the increased shakiness in the vicinity of such locus.…”