Computation of stiffness and stiffness bounds for parallel link manipulators

Parallel link spatial mechanisms in general, and Stewart Platforms in particular, are increasingly being studied for possible use in multi-axis machine-tools. An important consideration in the design of such machines is their stiffness. For a given design, stiffness varies with the direction in which it is computed, the posture (or configuration) of the mechanism and the direction of the actuation or disturbing force. This paper addresses the problem of finding the minimum and maximum stiffnesses and the directions in which they occur for a manipulator in a given posture. In addition, the computation of stiffness in an arbitrary direction is also discussed. Since engineers are often interested in the response of the mechanism in the direction of perturbation (called single-dimensional or engineering stiffness in this paper), this paper proves the computed bounds (maximum and minimum) are tight for such a definition. Stiffness computed using the algebraic formulae derived are compared to those obtained from a Finite Element Analysis model to demonstrate correctness of formulation. Finally, minimum, maximum, arbitrary direction and single-dimensional stiffness maps, are produced for a Stewart Platform and their use in machine tool design is discussed. (C) 1998 Elsevier Science Ltd. All rights reserved.