Experimental quasi-static crushing tests were conducted by using a universal testing machine format kenaf-epoxy composite elliptical cones. The work focused on the vertex angle's effects on energy absorption capab...Experimental quasi-static crushing tests were conducted by using a universal testing machine format kenaf-epoxy composite elliptical cones. The work focused on the vertex angle's effects on energy absorption capability; the vertex angles vary from 0° to 24° in 6 increments. The failure modes of the kenaf fibre epoxy composite elliptical cones were observed utilising delegate photos taken during the quasistatic crushing test. Load-deformation curves and deformation histories of typical specimens are presented and discussed. Moreover, the effects of cone vertex angles on the load carrying capacity and the energy absorption capability are also discussed. The results show that the energy absorption abilities significantly influence the ellipticity vertex angle as the load carrying capacity. We concluded that the quasi-static axial crushing behaviour of elliptical mat laminated composite cones is strongly affected by their structural geometry and the specific energy absorbed by the composite elliptical cones with vertex angles of 6°, 12°, 18°, and 24°, which is more than an elliptical cone with the vertex angle of 0°(the elliptical tube) at any given deformation. However, the specific energy absorption for the elliptical composite cone showed a positive correlation, i.e., the more the angle increased, the more energy was absorbed. In this regard, an elliptical composite cone with a 24° angle exhibited the best energy absorption capability.展开更多
Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given....Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.展开更多
Background: It has been postulated that elliptical cutaneous excisions must possess a length-to-width ratio of 3 to 4 and a vertex angle of 30o or less in order to be closed primarily without creating a “dog ear”. T...Background: It has been postulated that elliptical cutaneous excisions must possess a length-to-width ratio of 3 to 4 and a vertex angle of 30o or less in order to be closed primarily without creating a “dog ear”. These dimensions became axiomatic in cutaneous surgery and have been taught in the apprenticeship model for years. The present article examines the validity of that paradigm. Methods: We collected data from two sources: ellipses described in the literature (57 cases);and elliptical excisions performed at the authors’ outpatient clinic (83 cases). The surgical ellipse lengths, widths, and vertex angles were analyzed, and the data were compared to a mathematical formula used to generate a fusiform ellipse. Results: The length-to-width ratio of 3 - 4 was found to be inconsistent with the recommended vertex angle of 30o. In fact, a length-to-width ratio of 3 - 4 determines a vertex angle of 48o - 63o. A 30o vertex angle is only feasible with long length-to-width ration of about 7.5. Conclusions: The paradigm that surgical ellipses should have a vertex angle of 30o with length-to-width ratio of 3 - 4 is incorrect. Evidence from actual surgical practice and from mathematical formulation shows that either the length-to-width ratio must be larger than 3 - 4 or the vertex angle must be larger than 30 degrees.展开更多
According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high ord...According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high order perturbation normalizations. It is proved in the paper that when the renormalization effect of third order vertex angles process is taken into account, the symmetry of time reversal will be violated in electromagnetic interaction process. Because the magnitude order of symmetry violation is about 10–5, but the precision of current experiments on time reversal in particle physics is about 10–3, this kind of symmetry violation can not be found. The result reveals the micro-origin of asymmetry of time reversal and can be used to solve the famous irreversibility paradox in the evolution processes of macro- material systems.展开更多
由于六自由度机器人在装配序列规划中存在顶角叶片重力矩差难以保证、叶片重力矩分布不够均衡的问题,以至于避障过程中出现碰撞。为此,提出工业机器人六自由度装配序列规划下避障研究。通过分析六自由度机器人装配序列中,顶角叶片重力...由于六自由度机器人在装配序列规划中存在顶角叶片重力矩差难以保证、叶片重力矩分布不够均衡的问题,以至于避障过程中出现碰撞。为此,提出工业机器人六自由度装配序列规划下避障研究。通过分析六自由度机器人装配序列中,顶角叶片重力矩差和叶片重力矩分布产生的干涉关系,将装配平稳性、方向调整次数及更换装配工具的频次作为约束条件,设置干涉关系矩阵和适应度函数,以判断装配序列方案是否达到最佳;在装配方案达到最佳后,通过离散化萤火虫算法获取六自由度机器人装配序列最优解;根据该结果检测六自由度机器人碰撞结果,并采用优化随机树节点扩展控制及扩展能力检测的改进快速搜索随机树算法(Rapidly-exploring Random Tree,RRT*)来对所得装配序列进行调整修正,实现工业机器人六自由度装配序列规划下避障研究。实验结果证明:该方法可获取装配效率高、成本小的六自由度机器人装配序列;可以快速规划出最佳六自由度机器人避障路径,有效地避开障碍物,且精度较高、误差较小、实用性较强。展开更多
基金the Universiti Putra Malaysia for the financial support for this research programme using HiCoE Grant,Ministry of Higher Education,Malaysia
文摘Experimental quasi-static crushing tests were conducted by using a universal testing machine format kenaf-epoxy composite elliptical cones. The work focused on the vertex angle's effects on energy absorption capability; the vertex angles vary from 0° to 24° in 6 increments. The failure modes of the kenaf fibre epoxy composite elliptical cones were observed utilising delegate photos taken during the quasistatic crushing test. Load-deformation curves and deformation histories of typical specimens are presented and discussed. Moreover, the effects of cone vertex angles on the load carrying capacity and the energy absorption capability are also discussed. The results show that the energy absorption abilities significantly influence the ellipticity vertex angle as the load carrying capacity. We concluded that the quasi-static axial crushing behaviour of elliptical mat laminated composite cones is strongly affected by their structural geometry and the specific energy absorbed by the composite elliptical cones with vertex angles of 6°, 12°, 18°, and 24°, which is more than an elliptical cone with the vertex angle of 0°(the elliptical tube) at any given deformation. However, the specific energy absorption for the elliptical composite cone showed a positive correlation, i.e., the more the angle increased, the more energy was absorbed. In this regard, an elliptical composite cone with a 24° angle exhibited the best energy absorption capability.
基金Supported by the Doctoral Programs Foundation of Education Ministry of China（2011 3401110009） Supported by the Universities Natural Science Foundation of Anhui Province（KJ2013A220） Supported by the Natural Science Research Project of Hefei Normal University（2012kj11）
文摘Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.
文摘Background: It has been postulated that elliptical cutaneous excisions must possess a length-to-width ratio of 3 to 4 and a vertex angle of 30o or less in order to be closed primarily without creating a “dog ear”. These dimensions became axiomatic in cutaneous surgery and have been taught in the apprenticeship model for years. The present article examines the validity of that paradigm. Methods: We collected data from two sources: ellipses described in the literature (57 cases);and elliptical excisions performed at the authors’ outpatient clinic (83 cases). The surgical ellipse lengths, widths, and vertex angles were analyzed, and the data were compared to a mathematical formula used to generate a fusiform ellipse. Results: The length-to-width ratio of 3 - 4 was found to be inconsistent with the recommended vertex angle of 30o. In fact, a length-to-width ratio of 3 - 4 determines a vertex angle of 48o - 63o. A 30o vertex angle is only feasible with long length-to-width ration of about 7.5. Conclusions: The paradigm that surgical ellipses should have a vertex angle of 30o with length-to-width ratio of 3 - 4 is incorrect. Evidence from actual surgical practice and from mathematical formulation shows that either the length-to-width ratio must be larger than 3 - 4 or the vertex angle must be larger than 30 degrees.
文摘According to the current understanding, electromagnetic interaction is invariable under time reversal. However, the proof of time reversal symmetry in quantum theory of field has not considered the effects of high order perturbation normalizations. It is proved in the paper that when the renormalization effect of third order vertex angles process is taken into account, the symmetry of time reversal will be violated in electromagnetic interaction process. Because the magnitude order of symmetry violation is about 10–5, but the precision of current experiments on time reversal in particle physics is about 10–3, this kind of symmetry violation can not be found. The result reveals the micro-origin of asymmetry of time reversal and can be used to solve the famous irreversibility paradox in the evolution processes of macro- material systems.
文摘由于六自由度机器人在装配序列规划中存在顶角叶片重力矩差难以保证、叶片重力矩分布不够均衡的问题,以至于避障过程中出现碰撞。为此,提出工业机器人六自由度装配序列规划下避障研究。通过分析六自由度机器人装配序列中,顶角叶片重力矩差和叶片重力矩分布产生的干涉关系,将装配平稳性、方向调整次数及更换装配工具的频次作为约束条件,设置干涉关系矩阵和适应度函数,以判断装配序列方案是否达到最佳;在装配方案达到最佳后,通过离散化萤火虫算法获取六自由度机器人装配序列最优解;根据该结果检测六自由度机器人碰撞结果,并采用优化随机树节点扩展控制及扩展能力检测的改进快速搜索随机树算法(Rapidly-exploring Random Tree,RRT*)来对所得装配序列进行调整修正,实现工业机器人六自由度装配序列规划下避障研究。实验结果证明:该方法可获取装配效率高、成本小的六自由度机器人装配序列;可以快速规划出最佳六自由度机器人避障路径,有效地避开障碍物,且精度较高、误差较小、实用性较强。
