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Research Papers

Characteristic Equation-Based Dynamic Analysis of a Three-Revolute Prismatic Spherical Parallel Kinematic Machine

[+] Author and Article Information
Jun Zhang

School of Mechanical Engineering,
Anhui University of Technology,
Ma'anshan 243032, China
e-mail: junzhang@ahut.edu.cn

Jian S. Dai

Department of Informatics,
King's College London,
London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

Tian Huang

School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
e-mail: htiantju@public.tpt.tj.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 21, 2013; final manuscript received August 19, 2014; published online January 12, 2015. Assoc. Editor: Tae-Won Park.

J. Comput. Nonlinear Dynam 10(2), 021017 (Mar 01, 2015) (13 pages) Paper No: CND-14-1002; doi: 10.1115/1.4028416 History: Received November 21, 2013; Revised August 19, 2014; Online January 12, 2015

A three-revolute prismatic spherical (3-RPS) parallel kinematic machine (PKM) module is proposed as an alternative solution for high-speed machining (HSM) tool. Considering the PKM as a typical compliant parallel device, whose three limb assemblages have bending, extending, and torsional deflections, this paper applies screw theory to establish an analytical compliance model for the device. The developed compliance model is then combined with the energy method to deduce a comprehensive dynamic model of the 3-RPS module. The solution for the characteristic equations of the dynamic model leads to the modal properties of the PKM module. Based on the eigenvalue decomposition of the characteristic equations, a modal analysis is conducted. The natural frequencies and corresponding mode shapes at typical and nontypical configurations are analyzed and compared with finite element analysis (FEA) results. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of natural frequencies throughout the workspace are predicted to reveal a strong dependency of dynamic characteristics on mechanism's configurations. At the last stage, the effects of some design parameters on system dynamic characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement for the PKM.

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Figures

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Fig. 1

Structure of the 3-RPS module

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Fig. 2

Schematic diagram of the 3-RPS PKM

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Fig. 3

Assembly of an individual RPS limb

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Fig. 4

Spatial beam model of the limb body

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Fig. 5

FE-based modal properties of 3-RPS PKM at home position. (a) First-order and (b) second-order.

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Fig. 6

Natural frequencies distributions over the working plane at pz = 550 mm. (a) The first-order, (b) the second-order, (c) the third-order, (d) the fourth-order, (e) the fifth-order, and (f) the sixth-order.

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Fig. 7

Natural frequencies vary with ψ. (a) The first-order and (b) the second-order.

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Fig. 8

Natural frequencies vary with θ. (a) The first three orders and (b) the last three orders.

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Fig. 9

Variation of f¯1 with respect to pz and rp

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Fig. 10

Variation of f¯1 with respect to pz and rp

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Fig. 11

Variation of f¯1 with respect to rp and rb

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Fig. 12

f¯1 vary with limb body cross section

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