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Machine Theory
Mechanism and Machine Theory 43 (2008) 186–200
ate/mechmt
Stiffness analysis for a 3-PUU parallel kinematic machine
Yangmin Li *, Qingsong Xu
Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau,
Av. Padre Toma´s Pereira ., Taipa, Macao
Received 15 November 2005; received in revised form 20 April 2006; accepted 7 February 2007
Available online 6 April 2007
Abstract
This paper presents the stiffness characteristics of a three-prismatic-universal–universal (3-PUU) translational parallel
kinematic machine (PKM). The stiffness matrix is derived intuitively based upon an alternative approach considering actu-
ations and constraints, and pliances subject to both actuators and legs are involved in the stiffness model. The stiff-
ness performance of the manipulator is evaluated by utilizing the extremum stiffness values, and the influences of design
parameters on the stiffness properties are presented, which will be valuable for the architecture design of a 3-PUU PKM.
Moreover, the stiffness behavior of the PKM is investigated via the eigenscrew position of the stiffness matrix, which
provides a physical interpretation of the PKM stiffness and allows the identification of the stiffness center pliant
axis.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Parallel manipulators; Stiffness; Analysis; Workspace; Mechanism design
1. Introduction
In recent years, parallel manipulators have been investigated and developed more and more widely for var-
ious applications [1]. At the same time, less-DOF (degree-of-freedom) parallel manipulators with less than six
DOF have been applied extensively in many situations since they both maintain the inherent advantages of
parallel mechanisms and possess several other merits in terms of the total cost reduction in manufacturing
and operations [2–4].
Stiffness is one of the most important performances of parallel mechan