Cross-spring pivots, formed by crossing two identical flexural beams at their midpoint, have been broadly used in precision engineering and aerospace fields. Many researches have been conducted on modeling and analysi...Cross-spring pivots, formed by crossing two identical flexural beams at their midpoint, have been broadly used in precision engineering and aerospace fields. Many researches have been conducted on modeling and analysis of cross-spring pivots. However the influence of application position and magnitude of the external loads on the load-rotation and parasitic motion characteristics has not yet been discussed. In order to reveal the effect of the external loads, this paper develops the accurate load-rotation and center shift models of cross-spring pivots, with generalized planar loads applied including bending moment, horizontal and vertical forces. Firstly, by using the energy method, the load-displacement models of the pivot are derived with the assumption of small rotational angles. Based on the models, the influence of generalized planar loads on the load-rotation relationship is discussed, which shows that both application position and magnitude of the vertical and horizontal forces influence the load-rotation behaviors. Then the accurate center shift expressions of the pivot with generalized planar loads are developed, which shows that the rotational angle is the dominant term for both components of the center shift while the vertical and horizontal forces are small. Finally, the accuracy of the proposed model is validated by finite element analysis（FEA）. Comparing the model data with the results obtained from FEA, the relative error of the load-rotation is less than 6% even if the rotational angle reaches 20°; the relative errors of the two components of center shift are less than 5% and 10% respectively when the rotational angle reaches 10°. The proposed model and analytical conclusions can be used to analyze and preliminarily design the compliant mechanisms containing cross-spring pivots.展开更多
＂Power Shift＂ is used as the emerging Asia （emerging China and India） and declining US, European Union （EU） and Japan in the contemporary world. In parallel, it is used as raising territorial disputes and Xenoph...＂Power Shift＂ is used as the emerging Asia （emerging China and India） and declining US, European Union （EU） and Japan in the contemporary world. In parallel, it is used as raising territorial disputes and Xenophobia in Asia and Europe, especially in East Asia, Japan, China, and Korea. However, Asian economic development and high economic growth rate attracts the US and the EU to Asian region, not a conflict, and it demands Asian stable development, rather than unstable territorial disputes. Angas Maddison Statistics, International Monetary Fund （IMF） and World Bank also shows that China will surpass the USA by Purchasing power parity （PPP） based Gross domestic product （GDP） economically in 2015. The world of the 21st century is not unilateral, but multilateral or multipolar system, and the sift is already starting from the American continent to the Asian continent. How does it ensure the Asian stability and how does it guarantee the collaboration and prosperity between Asian countries and the world？ And how does the United States uses Asian pivot and Asian rebalance strategy？ The analysis of these policies are extremely important for considering the future of the world system. In this article, the author investigates the rise and fall of the great powers in the transition era, and develops economics, knowledge and science technology in the near future. Especially the author investigates the importance of making networks of the think-tanks, and to strengthen the relationship between nation states and regions under the conflict and antagonism.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos. 50975007, 51105014)PhD Programs Foundation of Ministry of Education of China(Grant No. 20091102110023)China Postdoctoral Science Foundation(Grant No. 20100480179)
文摘Cross-spring pivots, formed by crossing two identical flexural beams at their midpoint, have been broadly used in precision engineering and aerospace fields. Many researches have been conducted on modeling and analysis of cross-spring pivots. However the influence of application position and magnitude of the external loads on the load-rotation and parasitic motion characteristics has not yet been discussed. In order to reveal the effect of the external loads, this paper develops the accurate load-rotation and center shift models of cross-spring pivots, with generalized planar loads applied including bending moment, horizontal and vertical forces. Firstly, by using the energy method, the load-displacement models of the pivot are derived with the assumption of small rotational angles. Based on the models, the influence of generalized planar loads on the load-rotation relationship is discussed, which shows that both application position and magnitude of the vertical and horizontal forces influence the load-rotation behaviors. Then the accurate center shift expressions of the pivot with generalized planar loads are developed, which shows that the rotational angle is the dominant term for both components of the center shift while the vertical and horizontal forces are small. Finally, the accuracy of the proposed model is validated by finite element analysis（FEA）. Comparing the model data with the results obtained from FEA, the relative error of the load-rotation is less than 6% even if the rotational angle reaches 20°; the relative errors of the two components of center shift are less than 5% and 10% respectively when the rotational angle reaches 10°. The proposed model and analytical conclusions can be used to analyze and preliminarily design the compliant mechanisms containing cross-spring pivots.
文摘＂Power Shift＂ is used as the emerging Asia （emerging China and India） and declining US, European Union （EU） and Japan in the contemporary world. In parallel, it is used as raising territorial disputes and Xenophobia in Asia and Europe, especially in East Asia, Japan, China, and Korea. However, Asian economic development and high economic growth rate attracts the US and the EU to Asian region, not a conflict, and it demands Asian stable development, rather than unstable territorial disputes. Angas Maddison Statistics, International Monetary Fund （IMF） and World Bank also shows that China will surpass the USA by Purchasing power parity （PPP） based Gross domestic product （GDP） economically in 2015. The world of the 21st century is not unilateral, but multilateral or multipolar system, and the sift is already starting from the American continent to the Asian continent. How does it ensure the Asian stability and how does it guarantee the collaboration and prosperity between Asian countries and the world？ And how does the United States uses Asian pivot and Asian rebalance strategy？ The analysis of these policies are extremely important for considering the future of the world system. In this article, the author investigates the rise and fall of the great powers in the transition era, and develops economics, knowledge and science technology in the near future. Especially the author investigates the importance of making networks of the think-tanks, and to strengthen the relationship between nation states and regions under the conflict and antagonism.
