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2021 | OriginalPaper | Chapter

15. Correlation Between Track Generation and Synthesis of Mechanisms

Authors : Iulian Popescu, Xenia Calbureanu, Alina Duta

Published in: Problems of Locus Solved by Mechanisms Theory

Publisher: Springer International Publishing

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Abstract

A correlation is made between the generation of trajectories by mechanisms and the synthesis of those mechanisms when the trajectory is given. It is exemplified with the articulated quadrilateral mechanism, finding a nonlinear algebraic system with 9 equations and 9 constant unknowns, which are the parameters that define the mechanism. It is shown that this system cannot be solved with numerical analysis methods to provide exact solutions, so that approximate methods are used, given that the measurement of coordinates on the drawing introduces errors, so that the measured points are not sure on that curve. The methods used to roughly solve the system are indicated, but the solutions found cannot be applied because some negative or zero values result. This leads to the solution of the optimal synthesis, i.e. to optimization problems with nonlinear constraints, indicating approximate methods of solving. An example is also given of finding the mechanism that draws a straight-line segment imposed by 6 points, finding several mechanisms with different precisions. The Newton–Raphson algorithm was used, applicable to a nonlinear algebraic system with only 6 equations and 6 unknowns.

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Literature
1.
go back to reference Popescu I, Mîlcomete DC (2006) Cercetări privind sinteza şi optimizarea mecanismelor. Editura Sitech Popescu I, Mîlcomete DC (2006) Cercetări privind sinteza şi optimizarea mecanismelor. Editura Sitech
2.
go back to reference Popescu I (1977) Proiectarea mecanismelor plane. Ed. Scrisul Romanesc, Craiova Popescu I (1977) Proiectarea mecanismelor plane. Ed. Scrisul Romanesc, Craiova
3.
go back to reference Popescu I Analytic methods for synthesis of fourbar linkage for realisation of some imposed curves. In: SYROM'77, vol 1, part 3, pp 543–552 Popescu I Analytic methods for synthesis of fourbar linkage for realisation of some imposed curves. In: SYROM'77, vol 1, part 3, pp 543–552
4.
go back to reference Popescu I (1979) Analytic methods of synthesis of the plane mechanisms which outline imposed trajectories. In: “Proc. 5th world congress theoretical machinery and mechanics, Montreal, Canada, 1979, vol 2, The American Society of Mechanical Engineers, New York, pp 1062–1064 Popescu I (1979) Analytic methods of synthesis of the plane mechanisms which outline imposed trajectories. In: “Proc. 5th world congress theoretical machinery and mechanics, Montreal, Canada, 1979, vol 2, The American Society of Mechanical Engineers, New York, pp 1062–1064
5.
go back to reference Popescu I, Predoi M (1979) Metoda de analiza cinematica a mecanismelor, pe baza diagramelor cinematice si a functiilor spline cubice. In: Buletinul stiintific, seria tehnica-matematica, institutul de invatamint superior Sibiu, vol. II, pp 197–205 Popescu I, Predoi M (1979) Metoda de analiza cinematica a mecanismelor, pe baza diagramelor cinematice si a functiilor spline cubice. In: Buletinul stiintific, seria tehnica-matematica, institutul de invatamint superior Sibiu, vol. II, pp 197–205
6.
go back to reference Popescu I Metode iterative folosite la sinteza mecanismelor pentru traiectorii impuse. In: SYROM'81, vol I-1, pp 215–224 Popescu I Metode iterative folosite la sinteza mecanismelor pentru traiectorii impuse. In: SYROM'81, vol I-1, pp 215–224
7.
go back to reference Popescu I, Predoi M Sinteza mecanismelor prin folosirea metodei Broyden. In: “Lucrarile simpozionului proiectarea asistata de calculator PRASIC'82, Mecanisme si organe de masini”, vol I, pp 85–90, Brasov Popescu I, Predoi M Sinteza mecanismelor prin folosirea metodei Broyden. In: “Lucrarile simpozionului proiectarea asistata de calculator PRASIC'82, Mecanisme si organe de masini”, vol I, pp 85–90, Brasov
8.
go back to reference Predoi M, Popescu I Folosirea functiilor spline cubice de doua variabile la analiza si sinteza mecanismelor In: “Lucrarile simpozionului Proiectarea asistata de calculator PRASIC'82, 12–14 noiembrie—Mecanisme si organe de masini”, vol I, pp 109–114 Predoi M, Popescu I Folosirea functiilor spline cubice de doua variabile la analiza si sinteza mecanismelor In: “Lucrarile simpozionului Proiectarea asistata de calculator PRASIC'82, 12–14 noiembrie—Mecanisme si organe de masini”, vol I, pp 109–114
9.
go back to reference Artobolevskii II, Levitskii NI, Cerkudinov SA (1959) Sintez ploskih mehanizmov. Gosu. Izd. Fiz. Mat. Lit, Moskva Artobolevskii II, Levitskii NI, Cerkudinov SA (1959) Sintez ploskih mehanizmov. Gosu. Izd. Fiz. Mat. Lit, Moskva
10.
go back to reference Andreicenko GP (1983) Metod statisticeskih ispîtanii pri sinteze krivosipno—coromîslovogo mehanizma. Izvestia V.U.Z. Masinostroenie, nr. 12, Moskva, p 50 Andreicenko GP (1983) Metod statisticeskih ispîtanii pri sinteze krivosipno—coromîslovogo mehanizma. Izvestia V.U.Z. Masinostroenie, nr. 12, Moskva, p 50
11.
go back to reference Bagchi TP (1993) Taguchi methods explained—practical steps to robust design. New Delhi Bagchi TP (1993) Taguchi methods explained—practical steps to robust design. New Delhi
12.
go back to reference Gabriele GA, Ragsdell KM (1977) The generalized reduced gradient method. A reliable tool for optimal design. ASMEJ Engn. Indus. 99:394–400CrossRef Gabriele GA, Ragsdell KM (1977) The generalized reduced gradient method. A reliable tool for optimal design. ASMEJ Engn. Indus. 99:394–400CrossRef
13.
go back to reference Watanabe K (1992) Application of natural equations to the synthesis of curve genetating mechanisms. Mech. Mach. Theory 27:261–273CrossRef Watanabe K (1992) Application of natural equations to the synthesis of curve genetating mechanisms. Mech. Mach. Theory 27:261–273CrossRef
14.
go back to reference Cossalter V, Doria A, Pasini M, Scattolo C (1992) A simple numerical approach for optimum synthesis of a class of planar mechanisms. Mech. Mach. Theor. 27(3):357–366CrossRef Cossalter V, Doria A, Pasini M, Scattolo C (1992) A simple numerical approach for optimum synthesis of a class of planar mechanisms. Mech. Mach. Theor. 27(3):357–366CrossRef
15.
go back to reference Krishnamurty S, Turcic DA (1992) Optimal synthesis of mechanisms using nonlinear goal programing techniques. Mech. Mach. Theor. 27(5):599–612CrossRef Krishnamurty S, Turcic DA (1992) Optimal synthesis of mechanisms using nonlinear goal programing techniques. Mech. Mach. Theor. 27(5):599–612CrossRef
16.
go back to reference Yu-Kuang L, Ji-Chang Z A new optimum synthesis method of planar mechanisms for the generation of paths and rigid—body position. SYROM’85, vol I-1, pp 215–222 Yu-Kuang L, Ji-Chang Z A new optimum synthesis method of planar mechanisms for the generation of paths and rigid—body position. SYROM’85, vol I-1, pp 215–222
17.
go back to reference Popescu I. Optimizarea mecanismelor pentru traiectorii impuse. In: “Lucrarile simpozionului Proiectarea asistata de calculator PRASIC'82, 12–14 noiembrie—Mecanisme si Organe de masini”, vol I, pp 97–102 Popescu I. Optimizarea mecanismelor pentru traiectorii impuse. In: “Lucrarile simpozionului Proiectarea asistata de calculator PRASIC'82, 12–14 noiembrie—Mecanisme si Organe de masini”, vol I, pp 97–102
18.
go back to reference Popescu I (Aug 1983) The mechanisms optimization for trajectories and imposed associated positions. In: “Computer aided analysis and optimization of mechanical system dynamics”. University Of Iowa City, S.U.A Popescu I (Aug 1983) The mechanisms optimization for trajectories and imposed associated positions. In: “Computer aided analysis and optimization of mechanical system dynamics”. University Of Iowa City, S.U.A
19.
go back to reference Popescu I Probleme privind sinteza optimala a mecanismelor. In: The Fifth IFTOMM international symposium on linkages and computer aided design methods (Theory and Practice of Mechanisms), SYROM'89, Bucarest, Romania, July, 6–11, 1989, vol I 3, pp 721–728 Popescu I Probleme privind sinteza optimala a mecanismelor. In: The Fifth IFTOMM international symposium on linkages and computer aided design methods (Theory and Practice of Mechanisms), SYROM'89, Bucarest, Romania, July, 6–11, 1989, vol I 3, pp 721–728
20.
go back to reference Popescu I Rezultate obtinute la sinteza optimala a mecanismelor. In: SYROM'89, vol I 3, pp 713–720 Popescu I Rezultate obtinute la sinteza optimala a mecanismelor. In: SYROM'89, vol I 3, pp 713–720
21.
go back to reference Popescu Iulian. Accelerarea convergentei procesului de calcul la optimizarea mecanismelor . In MERO'91. Al X-lea simpozion national de roboti industriali, cu participare internationala, Bucuresti, 18–20 aprilie 1991, vol III, pp 793–802 Popescu Iulian. Accelerarea convergentei procesului de calcul la optimizarea mecanismelor . In MERO'91. Al X-lea simpozion national de roboti industriali, cu participare internationala, Bucuresti, 18–20 aprilie 1991, vol III, pp 793–802
22.
go back to reference Popescu I. Influenta aproximatiei initiale asupra convergentei, la optimizarea mecanismelor. In: MERO'91. Al X-lea simpozion national de roboti industriali, cu participare internationala, Bucuresti, 18–20 aprilie 1991, vol III, pp 813–822 Popescu I. Influenta aproximatiei initiale asupra convergentei, la optimizarea mecanismelor. In: MERO'91. Al X-lea simpozion national de roboti industriali, cu participare internationala, Bucuresti, 18–20 aprilie 1991, vol III, pp 813–822
23.
go back to reference Ermakov SM (1976) Metoda Monte Carlo şi probleme înrudite. Editura Tehnică, Bucureşti Ermakov SM (1976) Metoda Monte Carlo şi probleme înrudite. Editura Tehnică, Bucureşti
24.
go back to reference Doronin VI, Konnova GV (1978) Primenenie lineinovo metoda cvadraticeskovo priblijeniia dlia sinteza mehanizma. In Izvestia VUZ Maşinostroeniia. 10 Doronin VI, Konnova GV (1978) Primenenie lineinovo metoda cvadraticeskovo priblijeniia dlia sinteza mehanizma. In Izvestia VUZ Maşinostroeniia. 10
25.
go back to reference Jiag H, Jiang GK A new method of four—bar linkage synthesis with ten points using algebric curves. SYROM ’89, Bucureşti, pp 433–438 Jiag H, Jiang GK A new method of four—bar linkage synthesis with ten points using algebric curves. SYROM ’89, Bucureşti, pp 433–438
26.
go back to reference Mohsen MO Sznthesis of cupler curve generating mechanism. SYROM’81, Bucureşti, vol I-1, pp 159–170 Mohsen MO Sznthesis of cupler curve generating mechanism. SYROM’81, Bucureşti, vol I-1, pp 159–170
27.
go back to reference Hernandez A, Amezua E, Ajuria MB, Llorente JL (1994) Multiple points on the coupler curve of transitional four—hinge planar linkages. Mech. Mach. Theor. 29(7):1015–1032CrossRef Hernandez A, Amezua E, Ajuria MB, Llorente JL (1994) Multiple points on the coupler curve of transitional four—hinge planar linkages. Mech. Mach. Theor. 29(7):1015–1032CrossRef
Metadata
Title
Correlation Between Track Generation and Synthesis of Mechanisms
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_15

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