The Dimensional Synthesis of the Linear Delta Robot for a Force-Feedback Device

We perform the dimensional synthesis of a parallel manipulator to be used as a force-feedback device in a virtual reality application for surgeon training in prostate brachytherapy. For such brachytherapy operations, the characteristics of the required workspace point towards the architecture of the linear DELTA robot to be used as the force-feedback device to the surgeon. In this paper, we address the dimensional synthesis of the linear DELTA robot for the prescribed workspace. To this end, we propose the minimum relative kinematic sensitivity as an objective function, a kinematic performance index that is different from most of the commonly used metrics, i.e., manipulability and dexterity. The minimum relative kinematic sensitivity represents the ratio of the minimum to the maximum effect of a unity-bounded set of actuator displacements on the moving-platform pose. These extremum sensitivities are computed independently over the prescribed workspace. Thence, the dimensional synthesis problem consists in finding the robot dimensions that maximize the minimum relative kinematic sensitivity, so it is guaranteed within a narrow interval over the prescribed workspace. This optimization problem is nonconvex, which poses a challenge from the computational point of view. However, because of symmetry in the mechanism and other simplifications, the number of optimization variables is reduced to four. This allows a reasonably fine discretization of the search domain, giving the designers confidence that the ensuing local optimum is close to the global optimum.