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《China Mechanical Engineering》 2016-02
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Multiply Separated Position Synthesis of Function Generation Mechanism Based on Monad Vectors

Wang Chengzhi;Zhang Quanming;Wang Shuke;Zhou Qiu;Dai Ting;Jimei University;Forestry Bureau of Yongan;  
The relative motion differences of the monads were presented to model the systems of equations for kinematic function synthesis of planar linkages.The uniform formulae of the relative motion differences with 0-order to higher-order derivatives were constructed firstly,and then the new variables and corresponding special auxiliary equations of the monad vectors were used to eliminate trigonometric function,the angular unknowns and even their higher order angular unknowns.The monad vectors and their corresponding auxiliary equations could be directly used to construct synthesis systems for finitely,infinitesimally and multiply separated precision positions,and the systems were polynomial equations with smaller values of the total degrees.Applying the formulae to five and four multiply separated positions of function synthesis for pin-jointed four-bar planar linkages was discussed.Some cases of the multiply separated positions were exemplified and their differences between the generated y-value and required y-value were calculated and charted.The results show that the positions at finitely and infinitesimally separated positions were passed through exactly according to the required function.However,the y-values generated by the mechanism with the higher-order functional requirements may be no more close to the required y-value than those generated by the mechanism with the lower-order functional requirements at all 0-order positions in the required range.The procedure is simpler and the formulae of monad have the better modularity than the dyad and triad,and can be easily adapted to automatic modeling and solving the equations in a computer.
【Fund】: 福建省自然科学基金资助项目(2012J01225)
【CateGory Index】: TH112
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