Kinematic sensitivity analysis of a 3-DoF decoupled translational parallel mechanism with uncertainties in the passive joints

Numerous studies in the literature have investigated the kinematic sensitivity of parallel manipulators. In some of the foregoing researches, the influence of the uncertainty in the passive joints has also been taken into account. This paper proposes a comprehensive formulation for extracting an index standing for the kinematic sensitivity of a 3-DoF parallel mechanism, called Tripteron which was built for the first time at the Laval University, while assuming clearances in the passive revolute joints. Some previous studies have developed mathematical models for the kinematic and error amplification of the parallel mechanism under study by figuring out the relation between the joint clearances and the manipulation error in the position of the end-effector of the mechanism. Moreover, some other papers have suggested quantitative measures for describing the kinematic sensitivity of mechanical robots based on the result of a unit-norm error in the joint space, where separate translational and rotational indices have been deduced. However, as the parallel mechanism under study has only translational degrees of freedom, a single, global error amplification index can be derived denoting the maximum position variability of its end-effector due to a unit-norm error in the passive joints. Extracting such an index is the goal of this paper, which has been accomplished by combining the virtue of the two aforementioned sets of studies, i.e., incorporating the error models into the definition of the general kinematic sensitivity indices.