Industrial robots are mechanical manipulators whose dynamic characteristics are highly nonlinear. To control a manipulator which carries a variable or unknown load and moves along a planned path, it is required to compute the forces and torques needed to drive all its joints accurately and frequently at an adequate sampling frequency (no less than 60 Hz for the arm considered). This paper presents a new approach of computation based on the method of Newton-Euler formulation which is independent of the type of manipulator-configuration. This method involves the successive transformation of velocities and accelerations from the base of the manipulator out to the gripper, link by link, using the relationships of moving coordinate systems. Forces are then transformed back from the gripper to the base to obtain the joint torques. Theoretically the mathematical model is "exact. "A program has been written in floating point assembly language which has an average execution time of 4.5 milliseconds on a.PDP 11/45 computer for a Stanford manipulator. This allows an on-line computation within control systems with a sampling frequency no lower than 60 Hz. A further advantage of using this method is that the amount of computation increases linearly with the number of links whereas the conventional method based on Lagrangian formulation increases as the quartic of the number of links.
Despite numerous journalistic accounts, systematic quantitative evidence on economic conditions during the ongoing COVID-19 pandemic remains scarce for most low- and middle-income countries, partly due to limitations of official economic statistics in environments with large informal sectors and subsistence agriculture. We assemble evidence from over 30,000 respondents in 16 original household surveys from nine countries in Africa (Burkina Faso, Ghana, Kenya, Rwanda, Sierra Leone), Asia (Bangladesh, Nepal, Philippines), and Latin America (Colombia). We document declines in employment and income in all settings beginning March 2020. The share of households experiencing an income drop ranges from 8 to 87% (median, 68%). Household coping strategies and government assistance were insufficient to sustain precrisis living standards, resulting in widespread food insecurity and dire economic conditions even 3 months into the crisis. We discuss promising policy responses and speculate about the risk of persistent adverse effects, especially among children and other vulnerable groups.
The solubility of lithium salts in dimethyl carbonate ͑DMC͒ found in solid electrolyte interface ͑SEI͒ films was determined. The salt-DMC solutions evaporated, and the salts were transferred into water for ion conductivity measurements. The salts examined included lithium carbonate ͑Li 2 CO 3 ͒, lithium oxalate ͓͑LiCO 2 ͒ 2 ͔, lithium fluoride ͑LiF͒, lithium hydroxide ͑LiOH͒, lithium methyl carbonate ͑LiOCO 2 CH 3 ͒, and lithium ethyl carbonate ͑LiOCO 2 C 2 H 5 ͒. The salt molarity in DMC ranged from 9.6 ϫ 10 −4 mol L −1 ͑LiOCO 2 CH 3 ͒ to 9 ϫ 10 −5 mol L −1 ͑Li 2 CO 3 ͒ in the order of LiOCO 2 CH 3 Ͼ LiOCO 2 C 2 H 5 Ͼ LiOH Ͼ LiF Ͼ ͑LiCO 2 ͒ 2 Ͼ Li 2 CO 3. X-ray photoelectron spectroscopy measurements on SEI films on the surface of the negative electrode taken from a commercial battery after soaking in DMC for 1 h suggested that the films can dissolve. Separately, the heat of dissolution of the salts was calculated from computer simulations for the same salts, including lithium oxide ͑Li 2 O͒, lithium methoxide ͑LiOCH 3 ͒, and dilithium ethylene glycol dicarbonate ͓͑CH 2 OCO 2 Li͒ 2 :LiEDC͔ in both DMC and ethylene carbonate ͑EC͒. The results from the computer simulations suggested that the order in which the salt was likely to dissolve in both DMC and EC was LiEDC Ͼ LiOCO 2 CH 3 Ͼ LiOH Ͼ LiOCO 2 C 2 H 5 Ͼ LiOCH 3 Ͼ LiF Ͼ ͑LiCO 2 ͒ 2 Ͼ Li 2 CO 3 Ͼ Li 2 O. This order agreed with the experiment in DMC within the experimental error. Both experiment and computer simulations showed that the organic salts are more likely to dissolve in DMC than the inorganic salts. The calculations also predicted that the salts dissolve more likely in EC than in DMC in general. Moreover, the results from the study were used to discuss the capacity fading mechanism during the storage of lithium-ion batteries.
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