以对过约束的认识看自由度分析的历史发展  

Review on the Mobility Development History with the Understanding of Overconstraints

作　　者：卢文娟[1,2] 张立杰[1,2] 谢平[3] 张一同[1,2] 黄真[1,2] 

机构地区：[1]燕山大学河北省并联机器人与机电系统实验室,秦皇岛066004 [2]先进锻压成形技术与科学教育部重点实验室(燕山大学),秦皇岛066004 [3]燕山大学河北省测试计量技术及仪器重点实验室,秦皇岛066004

出　　处：《机械工程学报》2017年第15期81-92,共12页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51275438);河北省高等学校科学技术研究项目(QN2014175)资助项目

摘　　要：过约束的处理是自由度计算的关键也是瓶颈,探索统一的自由度计算公式已经历一百五十余年的历史,回顾整个发展历程,其间伴随着人们对过约束由无到有,由浅入深的认识。以自由度计算的核心——"过约束"为线索,贯穿整个自由度发展历史,介绍具有代表性的四十余种自由度公式,按照各自对过约束的处理方式将其分为三大类:原始的自由度公式、考虑机构阶的自由度公式以及考虑全部过约束的自由度公式,总结各类公式的特点、分析其历史地位,从一个新的角度了解自由度发展的历史,为能进一步找出研究工作将来的发展方向,同时提出具有通用性,实用性的自由度新理论奠定基础。The determination of overconstraint is always one of the key and difficult problems in mobility calculation. The research on unified-mobility-formula has experienced over 150 years. Recalling the entire development process, the understanding of overconstraint is a step-by-step process. According to the overconstraint, which is the most core question of mobility analysis, a review on the calculation of the mobility is introduced. More than forty approaches/formulas for mobility calculation presented in the literature are selected and grouped in three categories in accordance with their treatment for overconstraint： original mobility formula, the formula considering the rank of mechanism and the formula considering all the overconstraint. Furthermore the main characteristics are analyzed and summarized. The development history of mobility formulae is emphasized in a new perspective, which makes us identify the future direction of research and provides references for the introduction of new mobility approaches/formulas which are uniform and universal.

关 键 词：自由度公式 过约束 并联机构 集合求交 

分 类 号：TH112[机械工程—机械设计及理论]