Optimum synthesis of planar linkages using a strain-energy error function under geometric constraints. (English) Zbl 1281.70006
Summary: This paper presents an improved approach to the optimum dimensional synthesis of planar linkages based on an elastic strain-energy error function, according to which the optimum link dimensions are those which result in the minimum energy when the linkage is forced to comply with the synthesis data. This method is suitable for any kind of kinematic synthesis for any planar linkage. New features include geometric constraints in the links, and an effective way of modelling the position of frame joints. In addition, an overall improvement of convergence has been achieved through a new formulation of the error function and its minimization using two stages in the iterative process.
MSC:
| 70B15 | Kinematics of mechanisms and robots |
References:
| [1] | Da Lio, M.; Cossalter, V.; Lot, R.: On the use of natural coordinates in optimal synthesis of mechanisms, Mechanism and machine theory 35, No. 10, 1367-1389 (2000) · Zbl 1052.70503 · doi:10.1016/S0094-114X(00)00006-9 |
| [2] | Ceccarelli, M.; Vinciguerra, A.: Approximate four-bar circle-tracing mechanisms: classical and new synthesis, Mechanism and machine theory 35, No. 11, 1579-1599 (2000) · Zbl 1140.70316 · doi:10.1016/S0094-114X(00)00013-6 |
| [3] | Crocesi, S.; Pennestrì, E.: Kinematic synthesis of a curve-scribing mechanism for prescribed finite motion, Mechanism and machine theory 40, No. 1, 91-98 (2005) · Zbl 1122.70302 · doi:10.1016/j.mechmachtheory.2004.06.002 |
| [4] | Shi, Z.; Yang, X.; Yang, W.; Cheng, Q.: Robust synthesis of path generating linkages, Mechanism and machine theory 40, No. 1, 45-54 (2005) · Zbl 1060.70006 · doi:10.1016/j.mechmachtheory.2004.05.008 |
| [5] | Hongying, Y.; Dewei, T.; Zhixing, W.: Study on a new computer path synthesis method of a four-bar linkage, Mechanism and machine theory 42, No. 4, 383-392 (2007) · Zbl 1150.70002 · doi:10.1016/j.mechmachtheory.2006.05.003 |
| [6] | De Jalón, J. García; Serna, M. A.; Avilés, R.: Computer method for kinematic analysis of lower pair mechanisms: parts I and II, Mechanism and machine theory 16, 543-566 (1981) |
| [7] | Avilés, R.; Ajuria, M. B.; De Jalón, J. García: A fairly general method for the optimum synthesis of mechanisms, Mechanism and machine theory 20, 321-328 (1985) |
| [8] | Avilés, R.; Navalpotro, S.; Hernández, E.; Amezua, A.: An energy-based general method for the optimum synthesis of mechanisms, Journal of mechanical design (ASME) 116, No. 1, 127-136 (1994) |
| [9] | Vallejo, J.; Avilés, R.; Hernández, A.; Amezua, E.: Nonlinear optimization of planar linkages for kinematic syntheses, Mechanism and machine theory 30, No. 4, 501-518 (1995) |
| [10] | Avilés, R.; Ajuria, M. B. G.; Vallejo, J.; Hernández, A.: A procedure for the optimal synthesis of planar mechanisms based on nonlinear position problems, International journal for numerical methods in engineering 40, No. 8, 1505-1524 (1997) |
| [11] | Avilés, R.; Ajuria, M. B. G.; Bilbao, A.; Vallejo, J.: Lagrange multipliers and the primal-dual method in non-linear static equilibrium of multibody systems, Communications in numerical methods in engineering 14, 463-472 (1998) · Zbl 0913.73050 · doi:10.1002/(SICI)1099-0887(199805)14:5<463::AID-CNM165>3.0.CO;2-W |
| [12] | Avilés, R.; Ajuria, M. B. G.; Gómez-Garay, V.; Navalpotro, S.: Comparison among nonlinear optimization methods for the static equilibrium analysis of multibody systems with rigid and elastic elements, Mechanism and machine theory 35, No. 8, 1151-1168 (2000) · Zbl 1140.70382 · doi:10.1016/S0094-114X(99)00053-1 |
| [13] | Avilés, R.; Vallejo, J.; Ajuria, G.; Agirrebeitia, J.: Second-order methods for the optimum synthesis of multibody systems, Structural and multidisciplinary optimization 19, No. 3, 192-203 (2000) |
| [14] | Avilés, R.; Hernández, A.; Amezua, E.; Altuzarra, O.: Position, velocity, acceleration and Jerk analysis of linkages using the geometric stiffness matrix, Mechanism and machine theory 43, No. 8, 964-983 (2008) · Zbl 1156.70004 |
| [15] | Angeles, J.; Bernier, A.: The global least-square optimization of function-generating linkages, ASME journal of mechanisms, transmissions, and automation in design 109, No. 2, 204-209 (1987) |
| [16] | Akhras, R.; Angeles, J.: Unconstrained nonlinear least-square optimization of planar linkages for rigid-body guidance, Mechanism and machine theory 25, No. 1, 97-118 (1990) |
| [17] | Angeles, J.; Ma, O.: Performance evaluation of four-bar linkages for rigid-body guidance based on generalized coupler curves, ASME journal of mechanical design 113, No. 1, 17-24 (1991) |
| [18] | Sancibrián, R.; García, P.; Viadero, F.; Fernández, A.: A general procedure based on exact gradient determination in dimensional synthesis of planar mechanisms, Mechanism and machine theory 41, No. 2, 212-229 (2006) · Zbl 1101.70006 · doi:10.1016/j.mechmachtheory.2005.04.006 |
| [19] | Bai, S. P.; Angeles, J.: A unified input – output analysis of four-bar linkages, Mechanism and machine theory 33, 240-251 (2008) · Zbl 1169.70003 · doi:10.1016/j.mechmachtheory.2007.01.002 |
| [20] | Petuya, V.; Gutiérrez, J. M.; Alonso, A.; Altuzarra, O.; Hernández, A.: A numerical procedure to solve non-linear kinematic problems in spatial mechanisms, International journal for numerical methods in engineering 73, No. 6, 825-843 (2008) · Zbl 1195.70008 · doi:10.1002/nme.2110 |
| [21] | De Jalón, J. García; Bayo, E.: Kinematic and dynamic simulation of multibody systems: the real-time challenge, (1994) |
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