Abstract
In this paper, the systematic method is developed to synthesize planar closed kinematic chains with all the possible kinds of multiple joints according to given K-independent loops and up to total multiple joint factor Vmax. First, the structural synthesis method of multiple joint kinematic chains based on the combination of corresponding simple and multiple joints is presented. Then, the complete atlas database containing all valid multiple joints in closed fractionated kinematic chains with up to 5 independent loops and up to 12 links is established and illustrated. Further, corresponding all possible 14 types of multiple joint assortments up to K = 5 and up to total multiple joint factor Vmax = 8 are obtained and classified in the tables for the first time. Next, the structural analysis of multiple-jointed fractionated kinematic chains with various total multiple joint factors is conducted, and main structural parameters are determinated. Finally, based on atlas database of synthesized kinematic chains with multiple joints, the examples of creation of robot manipulators are provided.
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References
Norton RL (2003) Design of machinery: an introduction to the synthesis and analysis of mechanisms and machines. McGraw-Hill, Boston
Uicker JJ, Pennock GR, Shingley JE (2003) Theory of machines and mechanisms. Oxford University Press, New York
Crossley FRE (1964) A contribution to Gruebler’s theory in the number synthesis of plane mechanisms. ASME J Eng Industry 86(1):1–8
Dobrjanskyj L, Freudenstein F (1967) Some applications of graph theory to the structural analysis of mechanisms. ASME J Eng Industry 89(1):153–158
Yan HS, Hwang YW (1990) Number synthesis of kinematic chains based on permutation groups. Math Comput Modelling 13(8):29–42
Mruthyunjaya TS (1979) Structural synthesis by transformation of binary chains. Mech Mach Theory 14:221–231
Yan HS, Chiu YT (2015) On the number synthesis of kinematic chains. Mech Mach Theory 89(7):128–144
Yan HS (1998) Creative design of mechanical devices. Springer Verlag, Singapore
Tsai LW (1999) Robot analysis: the mechanics of serial and parallel manipulators. Wiley-Interscience, New York
Ceccarelli M (2004) Fundamentals of mechanics of robotic manipulation. Kluwer Academic Publishers, Dordrecht
Simoni R, Carboni AP, Martins D (2009) Enumeration of kinematic chains and mechanisms. Proc Inst Mech Eng Part C J Mech Eng Sci 223(4):1017–1024
Butcher EA, Hartman C (2005) Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: application to 12- and 14-bar single degree-of freedom chains. Mech Mach Theory 40(9):1030–1050
Ding HF, Huang P, Zi B, Kecskemethy A (2012) Automatic synthesis of kinematic structures of mechanisms and robots especially for those with complex structures. Appl Math Modelling 36(12):6122–6131
Ding HF, Zi B, Huang P, Kecskeméthy A (2013) The whole family of kinematic structures for planar 2-and 3-DOF fractionated kinematic chains. Mech Mach Theory 70(12):74–90
Yan HS, Hsu CH (1988) Contracted graphs of kinematic chains with multiple joints. Math Comput Modelling 10(9):681–695
Ding H, Zhao J, Huang Z (2010) Unified structural synthesis of planar simple and multiple joint kinematic chains. Mech Mach Theory 45(4):555–568
Hsu CH (1992) Enumeration of basic kinematic chains with simple and multiple joints. J Frankl Inst 329(4):775–789
Ding H, Yang W, Huang P, Kecskeméthy A (2012) Automatic structural synthesis of planar multiple joint kinematic chains. ASME J Mech Des, 135(9): 031006-1–031006-10
Ding H, Yang W, Zi B, Kecskeméthy A (2016) The family of planar kinematic chains with two multiple joints. Mech Mach Theory 99(5):103–116
Chu J, Zou Y (2014) An algorithm for structural synthesis of planar simple and multiple joint kinematic chains. Proc Inst Mech Eng Part C J Mech Eng Sci 228(12): 2178–2192
Pozhbelko V, Ermoshina E (2015) Number structural synthesis and enumeration process of all possible sets of multiple joints for 1-DOF up to 5-loop 12-link mechanisms on base of new mobility equation. Mech Mach Theory 90(8):108–127
Pozhbelko V (2016) A unified structure theory of multibody open, closed loop and mixed mechanical systems with simple and multiple joint kinematic chains. Mech Mach Theory 100(6):1–16
Berge C (2001) The theory of graphs. Dover Publications, Mineola, New York
Acknowledgements
The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011. The authors thank Associate Professor Aleksander Evnin for fruitful discussion on the graph theory.
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Kuts, E., Kuts, D., Pozhbelko, V. (2019). Structural Synthesis of 1-DOF up to 5-Loop Kinematic Chains with Multiple Joints and Its Analysis in Robotics. In: Rizk, R., Awad, M. (eds) Mechanism, Machine, Robotics and Mechatronics Sciences. Mechanisms and Machine Science, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-319-89911-4_15
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DOI: https://doi.org/10.1007/978-3-319-89911-4_15
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