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Research Papers: Design of Mechanisms and Robotic Systems

Parameter–Excited Instabilities of a 2UPU-RUR-RPS Spherical Parallel Manipulator With a Driven Universal Joint

[+] Author and Article Information
Guanglei Wu

School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: gwu@dlut.edu.cn

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 16, 2018; final manuscript received May 9, 2018; published online June 26, 2018. Assoc. Editor: Massimo Callegari.

J. Mech. Des 140(9), 092303 (Jun 26, 2018) (9 pages) Paper No: MD-18-1047; doi: 10.1115/1.4040351 History: Received January 16, 2018; Revised May 09, 2018

This paper presents the parametrically excited lateral instabilities of an asymmetrical spherical parallel manipulator (SPM) by means of monodromy matrix method. The linearized equation of motion for the lateral vibrations is developed to analyze the stability problem, resorting to the Floquet theory, which is numerically illustrated. To this end, the parametrically excited unstable regions of the manipulator are visualized to reveal the effect of the system parameters on the stability. Critical parameters, such as rotating speeds of the driving shaft, are identified from the constructed parametric stability chart for the manipulator.

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Figures

Grahic Jump Location
Fig. 1

The 2 UPU-RUR-RPS SPM: (a) CAD model, (b) a prototype that is used as an active spherical joint, and (c) application of a machine tool head in a drill point grinder [12] (Reprinted with permission from Elsevier © 2016)

Grahic Jump Location
Fig. 2

Parameterization of the 2 UPU-RUR-RPS asymmetrical SPM: (a) kinematic structure and (b) orientation of the MP

Grahic Jump Location
Fig. 4

Orientation representation of the MP with azimuth–tilt angles

Grahic Jump Location
Fig. 5

The isocontours of the stiffness indices with respect to the geometric parameter: (a) ψ = 30 deg, (b) ψ = 45 deg, and (c) ψ = 60 deg

Grahic Jump Location
Fig. 6

The critical velocities (rad/s) for the induced resonance with kθ = 0.5 Nm/rad and Jxy = 0.008 kg m2: (a) ψ = 30 deg, (b) ψ = 45 deg, and (c) ψ = 60 deg

Grahic Jump Location
Fig. 7

The unstable regions (dotted areas) with Ω0 = 16π rad/s, kθ = 0.5 N m/rad, Jxy = 0.008 kg m2: (a) ψ = 30 deg, (b) ψ = 45 deg, (c) ψ = 60 deg

Grahic Jump Location
Fig. 8

The unstable regions (dotted areas) with α = 45 deg, kθ = 0.5 N m/rad: (a) Jxy = 0.009 kg m2, Ω0 = 16π rad/s, (b) Jxy = 0.009 kg m2, Ω0 = 20π rad/s, and (c) Jxy = 0.007 kg m2, Ω0 = 20π rad/s

Grahic Jump Location
Fig. 9

The unstable regions (dotted areas) with α = 45 deg, kθ = 0.5 N m/rad, Jxy = 0.008 kg m2: (a) Ω0 = 20π rad/s and (b) Ω0 = 24π rad/s

Grahic Jump Location
Fig. 10

The unstable regions (dotted areas) with α = 45 deg, Jxy = 0.008 kg m2: (a) kθ = 0.4 N m/rad, Ω0 = 20π rad/s and (b) kθ = 0.6 N m/rad, Ω0 = 24π rad/s

Grahic Jump Location
Fig. 11

Stability chart θ–Ω0 of misalignment angle and shaft rotating speed, where kθ and Jxy are in the unit of (N m/rad) and (kg m2), respectively

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