Optimal Design and Modeling of Spatial Parallel Manipulators

Abstract

Parallel manipulators offer much higher rigidity and smaller mobile mass than their serial counterparts, thus allowing much faster and more precise manipulations. The main disadvantage of parallel robots is their small workspace in comparison to serial arms of similar size. Furthermore, the manipulability of parallel robots is often poor in some regions of the (already small) workspace. Another problematic issue is effective modeling of parallel robot dynamics, often needed for control algorithms. Dynamic algorithms developed for serial robots or general closed-loop mechanisms cannot be easily applied to parallel robots when the objective is real-time, dynamicmodelbased control. Therefore, in this work we investigate how to design parallel manipulators so that their workspace size and manipulability are maximized, and how to model parallel robot dynamics effectively. We develop a new performance index that combines measures of manipulability and workspace size, and a kinematic optimization process yielding a design that delivers the best compromise between manipulability and space utilization. Two examples are considered: the New University of Western Australia Robot (NUWAR) and the Linear Delta robot. Our experience in optimal design studies shows that the exhaustive search minimization algorithm is effective for as many as four independent design variables and presents a viable alternative to advanced non-linear programming methods. We develop a method based on Hamilton’s canonical equations to solve both the inverse and direct problems of dynamics for parallel robots. The method uses carefully chosen dependent coordinates, called here the coordinates of the extended space. The approach is shown to be computationally more efficient than the more common acceleration-based methods.