基于最小范数原理的夹紧力优化设计算法

秦国华; 张卫红

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基于最小范数原理的夹紧力优化设计算法

机械与动力工程 | 更新时间：2026-09-14

- 基于最小范数原理的夹紧力优化设计算法
- An Optimal Method to Clamping Force Determination Based on the Minimum Norm Principle
- 中北大学学报（自然科学版） 2011年32卷第4期页码：442-447
- 作者机构：
  
  1. 南昌航空大学航空与机械工程学院
  2. 西北工业大学中法并行工程联合实验室
- 作者简介：
- 基金信息：
  
  航空科学基金资助项目(2006ZE56006);中国博士后科学基金资助项目(20070411142);国家自然科学基金资助项目(10676028);江西省教育厅科学技术基金资助项目(2007-172);南昌航空大学博士启动基金资助项目(EA200503139)
- DOI：
  中图分类号：
- 纸质出版：2011
- 稿件说明：
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秦国华, 张卫红. 基于最小范数原理的夹紧力优化设计算法[J]. 中北大学学报（自然科学版）, 2011,32(4):442-447.

秦国华, 张卫红. An Optimal Method to Clamping Force Determination Based on the Minimum Norm Principle[J]. 2011, 32(4): 442-447.
秦国华, 张卫红. 基于最小范数原理的夹紧力优化设计算法[J]. 中北大学学报（自然科学版）, 2011,32(4):442-447. DOI：

秦国华, 张卫红. An Optimal Method to Clamping Force Determination Based on the Minimum Norm Principle[J]. 2011, 32(4): 442-447. DOI：

摘要

合理地确定夹紧力是夹具设计过程极为重要的环节

为此对工件处于稳定状态的约束条件进行了系统研究

提出了夹紧力的优化设计算法.首先

基于螺旋理论建立了工件稳定性模型.其次

基于最小范数原理

提出了夹紧力的优化设计模型.在摩擦锥线性转化以及变量非负转换的基础上

提出了夹紧力的优化设计松弛为线性规划问题的求解方法.最后

以典型的"3-2-1"定位方案为例

分析了其夹紧力优化设计的全过程.分析结果表明:基于最小范数原理的夹紧力优化算法简便易行

实验数据可靠

不但改变了一般工艺中夹具设计的经验性方法

而且也丰富了夹具设计的基础理论.

Abstract

It is important to determine the clamping forces correctly in the fixture design task.Therefore

constraint conditions of the workpiece stability were systematically investigated.Simultaneously

the optimal algorithm of clamping forces was proposed.Firstly

the mathematical model of workpiece stability was established on the basis of the screw theory.Secondly

the optimization of clamping forces was formulated according to the minimum norm principle.Based on the linear approximation of the friction cone and non-negative variable transformation

the solution technology was proposed by slacking the optimization of clamping forces into the constrained linear programming problem.Finally

took example for the typical "3-2-1" locating scheme

the optimal design procedure of clamping forces was illustrated.The analytical results show that the minimum norm principle based algorithm to clamping force optimization is effective and feasible

and the experimental data are verified to be reliable.The proposed method not only changes the experiential approach to fixture design in the traditional process planning

but also enriches the basic theory of fixture design.

关键词

Keywords

references

Cecil J.A clamping design approach for automated fixture design[J].International Journal of Advanced Manu-facturing Technology,2001,18:784-789.

熊蔡华,戴广宏,张传立,等.机械人多指手抓取的布局规划及其性能指标[J].江汉石油学院学报,1997,19(1):85-88.Xiong Caihua,Dai Guanghong,Zhang Chuanli,et al.Configuration planning of multifingered grasp and its stabilityindex[J].Journal of Jianghan Petroleum Stitute,1997,19(1):85-88.(in Chinese)

熊蔡华,熊有伦.机器人多指手协调操作中的约束运动及规划[J].华中理工大学学报,1994,22(9):39-44.Xiong Caihua,Xiong Youlun.Constrained motion and planning in coordination of multifinger robot hands[J].J.Huazhong Univ.of Sci.&Tech.,1994,22(9):39-44.(in Chinese)

Xiong C,Xiong Y.Stability index and contact configuration planning for multifingered grasp[J].Journal of RoboticSystems,1998,15(4):183-190.

秦国华,张卫红,万敏.基于线性规划的工件稳定性建模及其应用[J].机械工程学报,2005,41(9):33-37.Qing Guohua,Zhang Weihong,Wan Min.Modeling and application of workpiece stability based on the linearprogramming method[J].Chinese Journal of Mechanical Engineering,2005,41(9):33-37.(in Chinese)

Chou Y C,Chandru V,Barash M M.A mathematical approach to automatic configuration of machining fixtures:analysis and synthesis[J].ASME Journal of Engineering for Industry,1989,111(11):299-306.

Wang M Y,Liu Y H.Force passivity in fixturing and grasping[C].Proceedings of the 2003 IEEE InternationalConference on Robotics&Automation,Taipei,Taiwan,2003:2236-2241.

Wang M Y,Pelineascu D M.Contact forces prediction and force closure analysis of a fixtured rigid workpiece withfriction[J].ASME Journal of Manufacturing Science and Engineering,2003,125(2):325-332.

Xiong C H,Xiong Y L,Wang M Y.On prediction of passive contact forces of workpiece-fixture systems[C].ASME2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference Chicago,Illinois,USA,September,2003:1-10.

Trappey J C,Liu C R.An automatic workholding verification system[J].Robotics&Computer-Integrated Manu-facturing,1992,9(4):321-326.

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