Dynamic and Compliant Characteristics of a Cartesian-Guided Tripod Machine

[+] Author and Article Information
Jeng-Shyong Chen

Department of Mechanical Engineering, National Chung-Cheng University, Taiwan, ROC

Wei-Yao Hsu

Instrument Technology Research Center (ITRC), National Applied Research Laboratories (NARL), Taiwan, ROC

J. Manuf. Sci. Eng 128(2), 494-502 (Aug 26, 2004) (9 pages) doi:10.1115/1.1954789 History: Received July 29, 2003; Revised August 26, 2004

This paper is focused on the dynamic and compliant characteristics of a three-axis parallel kinematic machine called a Cartesian-guided tripod (CGT), which has a passive leg locking the platform three rotational degrees of freedom. Because no constraint mechanism is perfect with infinite rigidity, a compliance model has been developed to determine the maximum amplitude of the passive-leg parasitic motions using given loads. System compliance, dynamic characteristics, vibration modes, and servo-contouring errors of the CGT driving system have also been evaluated under high-speed machining conditions. The nonlinear dynamic effects, such as inertia and gravity, can be controlled within acceptable accuracy using the high-gain servo-feedback control techniques. The CGT dominant flexible mode occurs on the horizontal platform-leg vibration. The platform-leg flexible mode can produce significant jerk-induced mechanical vibration on the platform when a sudden velocity change is commanded. Look-ahead Cartesian-based path acceleration and deceleration control was found to be an efficient tool to reduce the jerk-induced mechanical vibration, although the CGT was drive controlled at the joint level. It was found that at high acceleration application, such as high-speed mold and die machining, the elastic elongation of the driving leg caused by the high acceleration force became the dominant contouring error sources.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

z3 head (Courtesy: DS Technologic)

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Figure 13

Comparison of the rigid and compliant models in the high-gain case

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Figure 14

Compliant-induced contouring error in a high-gain case

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Figure 15

Contour error in a circular path without ACC-DEC planning

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Figure 17

Frequency spectrum analysis of the result in Fig. 1

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Figure 3

CGT-based five-axis machine tool

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Figure 4

Cartesian-guiding mechanism

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Figure 11

CGT P-PI servo-control block diagram

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Figure 12

Contour error of rigid model with high gain and low gain

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Figure 16

Separated vibration components of the result in Fig. 1

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Figure 2

Tricept (Courtesy: Neso Robotics)

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Figure 5

Mass centers related to global origin

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Figure 6

Driving torques distribution on a Cartesian circular path

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Figure 7

The quantitative distribution of every inertia component

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Figure 8

Torsional compliant model of the driving system

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Figure 9

Axial complaint model of the driving system

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Figure 10

Complaint model of the passive leg



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