量化六自由度并联机构工作空间的六维超椭球体计算方法及其应用
收稿日期: 2015-05-07
修回日期: 2015-06-27
网络出版日期: 2015-07-27
基金资助
国家自然科学基金(51205195, 61403204);江苏省自然科学基金(BK20130981);南京林业大学高学历人才基金(GXL201316)
Calculation method and application of 6-D hyperellipsoid quantifying workspace of 6-DOF parallel manipulators
Received date: 2015-05-07
Revised date: 2015-06-27
Online published: 2015-07-27
Supported by
National Natural Science Foundation of China (51205195, 61403204); Natural Science Foundation of Jiangsu Province (BK20130981); Foundation for Advanced Degree Talents of Nanjing Forestry University (GXL201316)
基于头盔伺服系统执行机构的结构优化设计需求,提出了一种量化六自由度并联机构工作空间的六维空间超椭球体的计算方法,该方法的计算过程包括二维包络椭圆的求解和六维超椭球体的计算两部分。首先,重新总结和归纳了包络椭圆的定义,提出了包络椭圆的计算方法,在计算过程中提出了椭圆中心坐标修正步长、包络椭圆的两半轴长修正因子以及纵轴半轴长修正步长等概念,实现了对椭圆中心和半轴长的动态修正,提高了包络椭圆计算的准确性和智能化水平,采用调整系数来实时修改修正步长,保证了计算过程的收敛性;其次,给出了判定包络椭圆的条件和方法,方便了对计算方法有效性的验证;再次,提出了根据投影面内包络椭圆几何信息求解六维超椭球体的方法;最后,对包络超椭球体的计算方法进行了实例计算与验证,并通过实例计算对该方法用于六自由度并联机构工作空间优化的可行性和实用性进行了验证。结果表明:各投影面的包络椭圆均符合判定条件,即本文对包络椭圆与超椭球体的计算是准确的;优化结果对应的工作空间内接六维超椭球体能完全包含目标工作空间的包络超椭球体,即采用超椭球体来量化和优化六自由度并联机构工作空间是可行的,且具有较好的实用性。
李鹏 , 吴东苏 , 郑琰 , 施政 , 金兴悦 . 量化六自由度并联机构工作空间的六维超椭球体计算方法及其应用[J]. 航空学报, 2015 , 36(12) : 4001 -4013 . DOI: 10.7527/S1000-6893.2015.0190
A method to quantify the workspace of 6-DOF parallel manipulator using six-dimensional hyperellipsoid is proposed based on structural optimization requirements of helmet mounted display servo system. The method is made up of two parts:the calculation of two-dimensional circling ellipse and the computation of the corresponding hyperellipsoid. The former part is developed firstly, and the definition of circling ellipse and the corresponding conceptions are also proposed, such as modification step of the center and the longitudinal axis of circling ellipse, the modification factor of the axes' length of circling ellipse, etc. The dynamic modifications of the center and axes length of circling ellipse are implemented, and the accuracy and intellectual ability of the method are improved. The adjustment coefficients of modification step above are adopted to ensure the convergence of the calculation. Secondly, the conditions and methods to identify circling ellipse are developed, and the method of computing hyperellipsoid based on fifteen circling ellipse is also proposed. Finally, example to verify the validity of the novel method is developed, and the feasibility and practicability of the proposed method in workspace optimization are also tested. It is pointed out that circling ellipses calculated satisfy the identification conditions above, and the validity of the proposed method is better. Hyperellipsoid describing target workspace is contained completely by the other one which inscribes the workspace of optimization result, so the proposed method is feasible and practical for workspace optimization of 6-DOF parallel manipulator.
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