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Research Papers

Orientation Capability, Error Analysis, and Dimensional Optimization of Two Articulated Tool Heads With Parallel Kinematics

[+] Author and Article Information
Xin-Jun Liu

Institute of Manufacturing Engineering, Department of Precision Instruments, Tsinghua University, Beijing, 100084, People’s Republic of ChinaXinJunLiu@mail.tsinghua.edu.cn

Ilian A. Bonev1

Department of Automated Manufacturing Engineering, École de Technologie Supérieure, 1100 Notre-Dame St. W., Montreal, Quebec, H3C 1K3, CanadaIlian.Bonev@etsmtl.ca

1

Corresponding author.

J. Manuf. Sci. Eng 130(1), 011015 (Feb 15, 2008) (9 pages) doi:10.1115/1.2783255 History: Received November 09, 2006; Revised August 03, 2007; Published February 15, 2008

Because of the increasing demand in industry for A/B-axis tool heads, particularly in thin wall machining applications for structural aluminium aerospace components, the three-degree-of-freedom articulated tool head with parallel kinematics has become very popular. This paper addresses the dimensional optimization of two types of tool head with 3-P̱VPHS and 3-P̱VRS parallel kinematics (P, R, and S standing for prismatic, revolute, and spherical joint, respectively; the subscripts V and H indicating that the direction of the P joint is vertical or horizontal, and the joint symbol with underline means the joint is active) by considering their orientation capability and positioning accuracy. We first investigate the tilt angle of the spherical joint, the orientation capability, and the error of one point from the mobile platform caused by input errors. Optimization of the 3-P̱VPHS tool head is easy. For the 3-P̱VRS tool head, a design space is developed to illustrate how the orientation capability and error index are related to the link lengths. An optimization process is accordingly presented. Using the optimization method introduced here, it is not difficult to find all the possible optimal solutions.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Kinematic geometry of a general 3-[PP]S parallel mechanism

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Figure 2

Horizontal offset as a function of the orientation of a 3-[PP]S parallel mechanism

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Figure 3

Schematics of the two articulated tool heads: (a) with 3-P̱VPHS parallel kinematics and (b) with 3-P̱VRS parallel kinematics

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Figure 4

Tilt angle of a spherical joint: (a) a type of spherical joint, (b) this joint in a 3-P̱VPHS mechanism, and (c) this joint in a 3-P̱VRS mechanism

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Figure 5

Relationship between the tilt angle of a spherical joint and the orientation of the mobile platform: (a) for a 3-P̱VPHS tool head and (b) for a 3-P̱VRS tool head

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Figure 6

Orientation capability of a 3-P̱VRS tool head as limited by singularities only

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Figure 7

Error region in the o-xy plane for a given pose of the 3-P̱VPHS tool head

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Figure 8

Maximum error (in micron) versus platform orientation and the length l for a 3-P̱VPHS tool head: (a) maximum error for different orientation for l=1mm and (b) maximum error as function of l for ϕ=50deg and θ=20deg

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Figure 9

Proposed parameter design space for the 3-P̱VRS tool head

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Figure 10

Atlases for a 3-P̱VRS tool head: (a) orientation capability index (OCI) and (b) error index

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Figure 11

An identified optimum region when OCI >55deg and Ee_max<43μm

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