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Novel mobility formula for parallel mechanisms expressed with mobility of general link group

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Abstract

The determination of virtual constraints is always one of the key and difficult problems in traditional mobility calculation. To make mobility calculation simple, considering avoiding virtual constraints, some new formulae have been presented, however these formulae can hardly intuitively reflect general link group’s restrictions on output member and its influences on independence of output parameters, which is premise to the judgment of the properties of mobility. Towards the problem to reveal the intrinsic relationship between the degree of freedom(DOF) of a mechanism, the link group, and the dimension of output parameters, also to avoid determination of virtual constraint, based on the new concepts of the “DOF of general link group” and “node parameters”, a new formula in the calculation of the mobility of mechanisms is presented that is expressed with DOFs of the general link groups and rank of motion parameters of base point of the output link. It is named GOM(mobility of groups and output parameter) formula. On the basis of new concepts of “effective parameters” and “invalid parameters”, a rule is put forward for solving the DOF of mechanisms with invalid parameters by GOM formula, that is, the base point parameters are the subset of effective parameters of link group. Thereafter, several examples are enumerated and the results coincide with the prototype data, which proves the validity of the proposed formula. Meanwhile, it is obtained that the necessary and sufficient condition for the judgment of output parameters independence is that each of the DOF of the link group is not less than zero. The proposed formula which is simple in calculation provides theoretical basis for the judgment of independence of output parameters and provides references for type synthesis of novel parallel mechanisms with independence requirements of their output parameters.

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Authors and Affiliations

  1. Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao, 066004, China

    Yitong Zhang, Wenjuan Lu, Dejun Mu, Yandong Yang, Lijie Zhang & Daxing Zeng

Authors
  1. Yitong Zhang
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  2. Wenjuan Lu
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  3. Dejun Mu
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  4. Yandong Yang
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  5. Lijie Zhang
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  6. Daxing Zeng
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Corresponding author

Correspondence to Wenjuan Lu.

Additional information

This project is supported by National Natural Science Foundation of China(Grant Nos. 51275438, 51005195), Hebei Provincial Natural Science Foundation of(Grant No. E2011203214), and Development Program of Qinhuangdao City, China(Grant No. 201101A069)

ZHANG Yitong, born in 1945, is currently a professor at Yanshan University, China. He received his master degree in 1981. His research background is the theory and technology of cam. Since 2004, his research interests have been the theory in mobility of mechanisms, composition principle of mechanisms and type synthesis. He presents a novel mobility formula for parallel mechanisms using virtual-loop method.

LU Wenjuan, born in 1983, is currently a PhD candidate majored in mechatronics in Yanshan University, China. She received her master degree on mechanical design and theory in Yanshan University in 2008. Her research interests include parallel mechanism, type synthesis.

MU Dejun, born in 1967, is currently an associate professor at Yanshan University. She received her PhD degree from Yanshan Universtiy, China, in 2008. Her main research interests include parallel mechanism, control technology.

YANG Yandong, born in 1978, is currently a doctor candidate majored in mechatronics. His research interests include mechachonics engineering, robotics.

ZHANG Lijie, born in 1969, is currently a professor and a PhD supervisor at College of Mechanical Engineering, Yanshan University, China. His main research interests include parallel mechanism, optimal design of parallel robot.

ZENG Daxing, born in 1978, is currently an associate professor at Yanshan University, China. He received his PhD degree on mechatronic engineering in Yanshan University in 2008. His research interests include parallel mechanism, type synthesis and image processing.

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Zhang, Y., Lu, W., Mu, D. et al. Novel mobility formula for parallel mechanisms expressed with mobility of general link group. Chin. J. Mech. Eng. 26, 1082–1090 (2013). https://doi.org/10.3901/CJME.2013.06.1082

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  • DOI: https://doi.org/10.3901/CJME.2013.06.1082

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