• Title/Summary/Keyword: Ball-bar Equation

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Geometric Errors Estimation of a Rotary Table using Double Ball-bar (볼바를 사용한 회전 테이블의 기하학적 오차 추정)

  • Lee, Kwang-Il;Lee, Dong-Mok;Kweon, Sung-Hwan;Yang, Seung-Han
    • Journal of the Korean Society for Precision Engineering
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    • v.27 no.11
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    • pp.98-105
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    • 2010
  • In this paper, double ball-bar is used to estimate the geometric errors of a rotary table, which includes one-axial motion, two-radial motions and two-tilt motions, except the angular positioning error. To simplify the measurement procedures, three measurement steps have been designed and developed. At each measurement step, one end of the double ball-bar is fixed at the nose of spindle and the other end is located on the rotary table. And specific circular test path is planned to keep the distance between two balls as constant at ideal case. The relationship including the geometric errors of a rotary table and the measured distance between two balls which is distorted by the geometric errors is defined by using ball-bar equation. Each geometric error is modeled as $4^{th}$ order polynomial considering $C^1$-continuity. Finally the coefficients of polynomial are calculated by least-square method. Simulation is done to check the validation of the suggested method considering set-up errors and measurement noise. Suggested method is applied to estimate geometric errors of a rotary table of a 5-axis machine tool.

Measurement Method for Geometric Errors of Ultra-precision Roll Mold Machine Tool: Simulation (초정밀 롤 금형 가공기의 기하학적 오차 측정 방법: 모의실험)

  • Lee, Kwang-Il;Yang, Seung-Han
    • Journal of the Korean Society for Precision Engineering
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    • v.30 no.10
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    • pp.1087-1093
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    • 2013
  • In this study, a measurement method of double ball-bar is proposed to measure the geometric errors of an ultra-precision roll mold machine tool. A volumetric error model of the machine tool is established to investigate the effects of the geometric errors to a radius error and a cylindricity of the roll mold. A measurement path is suggested for the geometric errors, and a ball-bar equation is derived to represent the relation between the geometric errors and a measured data of the double ball-bar. Set-up errors, which are inevitable at the double ball-bar installation, also are analyzed and are removed mathematically for the measurement accuracy. In addition, standard uncertainty of the measured geometric errors is analyzed to determine the experimental condition. Finally, the proposed method is tested and verified through simulation.

Modeling for The Dynamics of 10 D.O.F Biped Robot (10자유도 이족 보행로봇 운동식의 모텔링)

  • 최형식;이호식;박용헌;전대원
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.343-343
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    • 2000
  • The conventional actuators with the speed reducer had weakness in supporting the weight of the body and leg itself. To overcome this, a new four bar link mechanism actuated by the ball screw was proposed. Using this, we developed a new type of 10 D.O.F biped robot. The dynamics model of the biped robot is investigated in this paper. In the modeling process, the robot dynamics are expressed in the joint coordinates using the Euler-Lagrange equation. Then, they are converted in to the sliding joint coordinates, and joint torques are expressed in the force along the sliding direction of the ball screw. To test modeling of the robot, a computer simulation was performed.

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Configuration sensitivity analysis of mechanical dynamics

  • Bae, Daesung
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.10 no.1
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    • pp.112-119
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    • 2001
  • Design sensitivity is an important is an important device in improving a mechanical system design. A continuum design consists of the shape and orientation design. This research develops the shape and orientation design sensitivity method. The configura-tion design variables of multibody systems define the shape and orientation changes. The equations of motion are directly differentiated to obtain the governing equations for the design sensitivity. The governing equation of the design sensitivity is formulated as an over determined differential algebraic equation and treated as ordinary differential equations on mani-folds. The material derivative of a domain functional is performed to obtain the sensitivity due to shape and orientation changes. The configuration design sensitivities of a fly-ball governor system and a spatial four bar mechanism are obtained using the proposed method and are validated against those obtained from the finite difference method.

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