Research Papers

Design and Development of a Two Degree-of-Freedom Rotational Flexure Mechanism for Precise Unbalance Measurements

[+] Author and Article Information
Zhao Hongzhe

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: hongzhezhao@gmail.com

Ren Siyuan

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: 1286935193@qq.com

Li Ming

P&T Research Center,
CRRC Tangshan Co., Ltd.,
Tangshan 063035, China
e-mail: sjc-liming@tangche.com

Zhang Shuqing

Beijing Institute of Control Engineering,
Beijing 100190, China
e-mail: zh_angshuqing@126.com

1Corresponding author.

Manuscript received September 22, 2016; final manuscript received April 15, 2017; published online May 17, 2017. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 9(4), 041013 (May 17, 2017) (8 pages) Paper No: JMR-16-1279; doi: 10.1115/1.4036610 History: Received September 22, 2016; Revised April 15, 2017

To measure unbalanced moments, the knife-edge is used as a support module in traditional platforms, but performances rapidly deteriorate as the edge is worn down. In this paper, considering the requirements of measurements, a two degree-of-freedom (DOF) flexure mechanism is, thus, presented to overcome this drawback. First, off-axis stiffness and manufacturability are improved qualitatively by means of configuration analysis. Then, four generalized cross-spring pivots are exploited in the 2DOF flexure mechanism, and the geometric parameters are analyzed to achieve approximately constant rotational stiffness and reduced center shift simultaneously, which benefits calibration procedure and measurement precision. Models are further developed to determine the shape parameters of leaf-springs and transducer performances. Therefore, a low rotational stiffness is obtained to ensure a high resolution for measurements, and a high load-carrying capacity is achieved via strength checking. Finally, finite element analysis (FEA) is carried out to validate the proposed design, and experimental results demonstrate that the developed platform is capable of unbalance measurements with a high precision and resolution.

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Fig. 2

Two configurations of 2DOF rotational mechanism: (a) configuration 1 and (b) configuration 2

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Fig. 1

Principle of a 1DOF measurement platform: (a) measurement platform and (b) two candidates for support module

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Fig. 3

A generalized cross-spring pivot

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Fig. 4

Assembly process of the proposed 2DOF flexure mechanism

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Fig. 5

Parameter definitions of a generalized cross-spring pivot

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Fig. 7

Prototype of the flexure measurement platform: (a) measurement platform—(1) base, (2) electronic analytical balance-y-axis, (3) tare weight for y-axis, (4) flexure mechanism, (5) working platform, (6) payloads, (7) bubble level, (8) calibrated steel ball, (9) plate with calibrated concaves, (10) tare weight for x-axis, (11) electronic analytical balance-x–axis, and (b) flexure mechanism

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Fig. 8

Relationship between unbalanced moment and measurement error

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Fig. 6

FEA model of the 2DOF flexure mechanism: (a) under minimum unbalanced moment and (b) under maximum unbalanced moment



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