Kinematic Sensitivity of a Very Large Cable-driven Parallel Mechanism

The LAR is a concept of a large orientable radiotelescope composed namely of a cable-driven parallel mechanism used to position and orient a feed plate. This document presents a first analysis of this mechanism’s orientation capability. The rotational kinematic sensitivity is defined here as the possible change in orientation occuring under a change in the actuation. After the application is described, common tools related to such problems are reviewed to explain why they are not totally suitable in this context. The velocity equation of the mechanism is then partitioned to obtain a quantification of the orientation kinematic sensitivity that is physically relevant. The study of a potential architecture’s rotational kinematic sensitivity is presented. Finally, the numerical and experimental validation of the approach are discussed. INTRODUCTION: THE LAR PROJECT The Large Adaptive Reflector (LAR), shown in figure 1, is a large orientable radio antenna concept being developed as a possible sub-element of a next generation radiotelescope called the Square Kilometer Array (SKA). The LAR appellation is due to the nature of its primary reflector, a section of a low curvature parabola made of several actuated triangular panels. The actuation enables the orientation of the reflecting surface towards the desired part of the sky. Legg first suggested such an approach in [12]. Its goal is to lower the cost per collecting unit area and to circumvent the structural limit of the current construction method for large orientable dishes. This is achieved by keeping the reflector close to the ground. The challenge of building such an antenna compared to building conventional ones is that the receiver feed is not rigidly attached to the reflector and so it must be positioned and oriented 1 Figure 1 Artist representation of the LAR. independently at a precision that depends on the wavelength observed, the technology used for the feed, and the optical arrangement. Also, because the reflector has a low curvature, its focal length is large. For the present LAR concept, this distance at which the feed must be placed from the centre of the reflector is 500 m. Dewdney and Veidt presented in [4] a first refinement to Legg’s initial suggestion. They concluded that a promising way to position the feed plate is to use a cable-driven parallel mechanism kept under tension by an aerostat filled with helium. This possibility was studied in more detail in [3] where the authors suggested the use of another level of actuation (the confluence point mechanism, CPM) at the focal apparatus to obtain the precision needed. The complete feed positioning system they envisioned is shown schematically in figure 2. It consists of two parallel mechanisms mounted in series. The large cable mechanism links the ground to the confluence point (CP) structure and performs coarse positioning and orientation Copyright © 2006 by ASME Large Mechanism CP Structure CPM Aerostat Leash Incoming radio waves